zilongwang/ReadingBank huggingface dataset:
Geomant Contact Expert is a cost-effective, fully featured, multichannel, contact center solution that is tightly integrated with Microsoft Lync Server 2010. For customer-facing organizations requiring a cost-effective but feature-rich contact center solution, Geomant offers Contact Expert, which drives improved productivity and customer service. Unlike more complex solutions, Contact Expert is a solution, designed for Microsoft Lync voice environments, and it is ideal where a subset of Lync users require contact center capabilities. Business Needs Contact Center technology improves customer service and organizational productivity. But the cost of such solutions is often prohibitive, particularly for small and medium enterprises. There is a need for a cost-effective, fully featured multichannel contact center solution, designed to complement Microsoft Lync Server 2010. Solution Geomant Contact Expert is a complete solution that encompasses inbound, outbound, and blended contact center environments, and includes call recording and full reporting features. Closely integrated with Microsoft Lync, it is suitable for organizations of all sizes. Because it is designed for Windows Server environments, Contact Expert provides simple integration to business applications. Contact Expert combines rapid deployment with simple configuration. Its sophisticated software-based Automatic Call Distribution capabilities ensure maximum productivity and enhanced customer service. Organizations can define, implement, and tune multiple campaigns, using multiple channels—voice, email, and short message service (SMS). All telephony functions are achieved through the Lync platform. When agents log on to Contact Expert, they are automatically logged on to Lync Server 2010. Calls can then be initiated, answered, placed on hold, transferred, or escalated to conference status. Geomant Contact Expert features include: Automatic Call Distribution, with multiple routing strategies. Multichannel capability for voice, email, and SMS. Campaign management for defining, implementing, and tuning multiple inbound and outbound campaigns. Interactive voice response (IVR) for fronting calls or deploying full self-service applications. Integration with business applications. Call recording for compliance and quality. Inbound, outbound, and blended support. Distributed architecture for scalability and resilience. Full and flexible reporting, both real-time and historic. Software-based wallboard for agents and supervisors. Built-in softphone that manages Lync telephony functions. Skills-based routing and expert call transfer. Simple creation of campaign flows and IVR scripts
Geomant SMS for Microsoft Lync makes it possible for users to send SMS text messages directly from Microsoft Lync 2010. Geomant SMS for Microsoft Lync helps organizations improve internal and external communications by adding outbound Short Message Service (SMS) text messaging as a communications channel. Users initiate SMS text messages from Microsoft Lync 2010 and can send them to both individuals and groups. Business Need Many organizations use SMS text messaging for person-to-person communications or for initiating broadcast messages to groups of people. Users want to send SMS text messages with the communications tools they use every day. Solution Geomant SMS for Microsoft Lync makes it possible for users to send SMS text messages from the Microsoft Lync 2010 client interface. Users can send messages to one or multiple contacts, which is ideal when Lync contacts are offline. The solution works with customers’ own SMS gateways or through public or carrier SMS gateways, using standard messaging protocols SMTP and SMPP. Features include the following: Send SMS messages to existing and new contacts from within Lync 2010. Open a new SMS window by right-clicking any user on the contact list. Use the simple interface to add single contacts, multiple contacts, or contact groups to the SMS recipient list. Receive confirmation of successful SMS initiation. Reach Lync contacts who are not currently online. Confirm information following an instant messaging (IM) conversation. Deliver messages so they appear to come from the initiator’s mobile phone, allowing replies to be sent directly to that mobile phone. Components include the following: Client application: The client application allows SMS text messages to be initiated from the contact list or during a conversation. Server application: The server application interfaces with Lync 2010 and initiates outbound SMS text messages. SMS application programming interface (API): The API integrates with most commercial on-premises SMS gateways.
Lidar classifications: Class 1 – Unclassified Class 8 – Model key Class 2 – Bare-earth ground Class 9 – Water Class 3 – Low vegetation Class 10 – Ignored ground Class 4 – Medium vegetation Class 11 – Reserved Class 5 – High vegetation Class 12 – Overlap Class 6 – Building Class 13 – Reserved (bridges) Class 7 – Low point (noise) Class 14 – Reserved (culverts) Attached Items from Participant Required: Signed Letter of ‘Intent to Participate’ Required: Project Boundary – USGS Square Mile Grids (in ESRI Feature Class/Shapefile or KML format) Optional: Customer-supplied data (elevation data, ground control, etc.) Contact Information (Name, Title, Direct Phone, E-Mail) Special Requirements (attach add’l document if necessary)
EXAMPLE: The number of buttons on each of 10 shirts is shown in the probability distribution below: Number of buttons 4 5 6 Frequency 1 5 Probability 1/10 5/10 #1. Complete the missing parts of the table. #2. What is the probability that a shirt chosen at random from the set of 10 shirts has 5 buttons? #3. What is the sum of the probabilities? #4. What is the probability of randomly choosing a shirt that has more than 4 buttons from a set of 10 shirts? We finally want to learn about a type of a probability called a conditional probability. A conditional probability is the probability that an event will occur, given that another event has ALREADY occurred. You can write the conditional probability of event B, given that event A has already occurred as: The above is read as: “the probability of event B, given event A.” EXAMPLE: Opinion polls: Respondents of a poll were asked whether they were for, against or had no opinion about a bill before the state legislature that would increase the minimum wage. What is the probability that a randomly selected person is over 60 years old, given that the person had no opinion on the state bill? Age Group For Against No Opinion TOTALS 18-29 310 50 20 380 30-45 200 30 10 240 45-60 120 20 30 170 Over 60 150 20 40 210 TOTALS 780 120 100 1000 #1. What is the probability that a person randomly selected has over 60 years old given that they have no opinion? #2. What is the probability that a randomly selected person is 30-45 years old, given that the person is in favor of the minimum wage bill? #3. What is the probability that a randomly selected person is NOT 18-29, given that the person is in favor of the minimum wage bill? #4. What is the probability that a randomly selected person is AGAINST the minimum wage bill? #5. What is the probability that a randomly selected person is FOR the minimum wage bill, given that they are 30-45 years old? #6. What is the probability that a randomly selected person is 18-29 years old, given that they have no opinion of the minimum wage bill?
____ 38. What is the graph of ? A. C. B. D. ____ 39. Write an equation in slope-intercept form of the line through point P(6, –1) with slope 4. A. y = 4x – 1 C. y + 1 = 4(x – 6) B. y = 4x – 25 D. y + 6 = 4(x – 1) 40. What is an equation in slope-intercept form for the line given? ____ 41. Write the equation for the vertical line that contains point E(–7, 7). A. y = 7 B. x = –7 C. y = –7 D. x = 7 ____ 42. Write the equation for the horizontal line that contains point G(3, 4). A. x = 4 B. y = 4 C. y = 3 D. x = 3 43. What is an equation in point-slope form for the line perpendicular to y = 2x + 13 that contains (8, –4)? ____ 44. Are the lines y = –x – 2 and 4x + 4y = 16 perpendicular? Explain. A. Yes; their slopes have product –1. B. No; their slopes are not opposite reciprocals. C. Yes; their slopes are equal. D. No; their slopes are not equal ____ 45. Are the lines y = –x – 4 and 2x – 2y = 10 perpendicular? Explain. A. Yes; their slopes are equal.
You could live in a house in the suburbs or country ____ 10. What is the converse of the following conditional? If a point is in the first quadrant, then its coordinates are positive. If the coordinates are positive, then a point is in the first quadrant. ____ 11. For the following true conditional statement, write the converse. If the converse is also true, combine the statements as a biconditional. If x = 4, then 4x = 16. Converse: If 4x = 16, then x = 4. True x = 4 if and only if 4x = 16 ____ 12. What is the converse of the following true conditional? The inverse? The contrapositive? If two lines are parallel, they do not intersect. Converse: If 2 lines do not intersect, then they are parallel. Inverse: If 2 lines are not parallel, then they do intersect. Contra: If 2 lines do intersect, then they are not parallel. ____ 13. Determine whether the conditional and its converse are both true. If both are true, combine them as a biconditional. If either is false, give a counterexample. If an angle is an acute angle, its measure is less than 90. If an angle measure is less than 90, the angle is an acute angle. Both are True Biconditional: An angle is an acute angle if and only if its measure is less than 90. ____ 14. Write the two conditional statements that make up the following biconditional. I drink coffee if (and only if) it is breakfast time. If I drink coffee, then it is breakfast time. If it is breakfast time, then I drink coffee. ____ 15. One way to show that a statement is NOT a good definition is to find a ____. Counterexample ____ 16. Provide a counterexample to the following faulty definition? A square is a figure with four sides. A rectangle (or rhombus, parallelogram, trapezoid) has four sides as well.
____ 20. What is the value of x? Identify the missing justifications. , , and . a. Angle Addition x + 7 + x + 3 = 100 b. Substitution Property 2x + 10 = 100 c. Simplify 2x = 90 d. Subtraction x = 45 e. Division Property of Equality ____ 21. bisects = 6x. = 2x + 24. Find 6x = 2x + 24 + 2x + 24 (You must double the small angle to get the 6x) 6x = 4x + 48 2x = 48 x = 24 DBC = 2(24) + 24 = 72 ____ 22. Use the Transitive Property of Congruence to fill in the blank. If ______. ____ 23. Use the Substitution Property of Equality to fill in the blank. If , then ______. 8x + 3 = 12 ____ 24. Name the Property of Congruence that justifies the statement: If . Symmetric ____ 25. Name the Property of Congruence that justifies this statement: If . Transitive ____ 26. Complete the two-column proof. Given: Prove:
Geometry Chapter 1: Points, Lines, Planes and Angles 1.1 Points, Lines and Planes Bell Ringer: (Integer / substitution review for PLAN) Order of Operations Addition & Subtraction of Integers Rules for Multiplication & Division of integers Examples Undefined Terms Point Line Line segment Plane objectives: -identify and model points, lines and planes -identify collinear and coplanar points intersecting lines and planes in space If a = -2 and b = -4 then a2b + 2ab = ? A. 0 B. 4 C. 16 D. 32 E. 40 Show your work: Evaluate the given expressions 1) z(x+y); use x=6, y=-8 and z=6 2)If m=-8 and q = -3 then 6q + 2m – m = ? 3) p3+10+m; use p=-2 m=-9 4) If m=4 and p=-7 then p2m/4=?
1.4 Angle Measure Bell Ringer: ray opposite rays angle Protractor and degrees Types of angles Examples Congruent angles Angle bisectors ____________________________________________________________________________ What did we learn in this lesson? What do I want to understand better? objective: -identify and use special pairs of angles -identify and use perpendicular lines ____________________________________________________________________________ Algebra Review Slip __________________________________________________________________________ Adjacent Angles – Vertical Angles – Linear pairs – Complementary Angles – Supplementary Angles –
Examples Summary: Assignment 1.5 page 42 Find the length of each side of the polygon for the given perimeter. 1. 2. COORDINATE GEOMETRY Find the perimeter of quadrilateral OPQR with vertices O(-3, 2), P(1, 5), Q(6, 4), and R(5, -2)
G-GMD.A.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments. Not included in the course. G-GMD.B.4 Identify the shapes of two-dimensional cross-sections of objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. Not included in the course.
Vocabulary: You are responsible for the following terms, theorems and postulates. collinear Points coplanar Points ray plane line line Segment segment addition postulate segement subtraction postulate midpoint bisect acute angle right angle obtuse angle straight angle angle bisector complementary angles Parallel Lines Perpendicular Lines Skew Lines Parallel Planes Perpendicular Planes Corresponding angles a. Postulate b. Converse Alternate interior angles a. Theorem b. Converse Alternate exterior angles a. Theorem b. Converse Consecutive interior angles a. Theorem b. Converse Right Triangle Scalene Triangle Equilateral Triangle Equiangular Triangle Acute Triangle Isosceles Triangle Obtuse Triangle Exterior Angle Theorem Base Angles Theorem Converse Hinge Theorem Converse Triangle Inequality Theorem Perimeter Area of Triangle Midsegment supplementary angles adjacent angles linear pair vertical angles linear pair postulate vertical angle theorem polygon equilateral equiangular regular polygon concave polygon convex polygon interior angles exterior angles conditional converse inverse contrapositive Triangle Congruence Postulates: SSS SAS HL ASA AAS Theorem Perpendicular Bisector Median Altitude Points, lines and planes For questions 1-9, use the diagram to determine if the statement is true or false.
Answer Key: false false true true false false true true false x = 12.5 m∢1 = 127° x = 6 m∢PAT = 50° m∢1 = 37° m∢2 = 143° m∢1 = 18° m∢2 = 72° multiple answers multiple answers multiple answers ∢ADF and ∢FDB OR ∢BXD and ∢DXA multiple answers D a) x = 9 b) 8° a) = 21 b) not a midpoint = 9 a) x = 9.5 b) = 70 (2, 1) (8, 11) none none none 80° 60° 62° x = 10 x = 6 If two angles are congruent, then they are vertical. If two angles are not vertical then they are not congruent. If two angles are not congruent, then they are not vertical. No; the converse is not true. contrapositive 80° = 5cm 70° 78ft 48in m∢G = 56° m∢H = 76° m∢I = 48° 3 < x < 13 150° 30° x = 35 x = 13 SAS HL
AAS NEI NEI AAS SAS NEI Statements Reasons C is the midpoint of , , Given Definition of Midpoint ∢B ≅ ∢C Corresponding Angles Postulate ∆DAC ≅ ∆FCB SAS CPCTC Statements Reasons bisects, , bisects ∢FDG Given Definition of Bisect ∢FDB ≅ ∢BDG Definition of Bisect ∢EDA ≅ ∢BDG Vertical Angle Theorem ∢FDB ≅ ∢EDA Transitive Property ∆EDA ≅ ∆FDB SAS ∢A ≅ ∢B CPCTC x = 25.7 y = 22.9 x = 7 y = 16 sometimes never sometimes never always sometimes always never sometimes sometimes always sometimes a) b) c) none d) e) a) x = 6 b) y = 20 c) = 17 a) b) c) d) e) is a midsegment of ∆ABC because it is both parallel to and half the length of .
not equilateral concave not a polygon convex Polygon Sum of Interior Angles Sum of Exterior Angles Heptagon 900° 360° Dodecagon 1800° 360° 15-gon 2340° 360° Regular Polygon Each Interior Angle Each Exterior Angle Octagon 135° 45° Decagon 144° 36° 20-gon 162° 18° octagon 36-gon decagon pentagon 72-gon nonagon 158° = 49 x = 0.5 x = 4 y = 24 x = 12 x = 10 x = 3
Grade: Geometry Enduring Skill 2: Students develop understanding of congruence. Demonstrators : Students establish triangle congruence criteria. (G.CO.7, G.CO.8) 2. Use triangle congruence as a familiar foundation for the development of formal proof. (G.CO.10, G.CO.11, G.SRT.4) 3. Use congruence to solve problems. (G.SRT.5) Assessment Items: ES 2, Demonstrator 2, Standards (G.CO.10, G.CO.11, G.SRT.4) Given: In the proof shown above, which postulate or theorem justifies step 6? CPCTC SSS Postulate SAS Postulate Alternate Interior Angle Theorem
Geometry Enriched Midterm Review 2015 The following sections will be included on your midterm. Chapter 1 – Tools of Geometry 1-1 – Points, lines, and Planes 1-2 – Linear Measure 1-3 – Distance and Midpoint 1-4 – Angle Measure 1-5 – Angle Relationships Chapter 2 – Reasoning and Proof 2-1 – Inductive Reasoning ad Conjecture 2-2 - Logic 2-3 – Conditional Statements 2-4 - Deductive Reasoning 2-5 – Postulates 2-6 – Algebraic Proof 2-7 – Proving Segment Relationships 2-8 – Proving Angle Relationships Chapter 3 – Parallel and Perpendicular Lines 3-1 – Parallel Lines and Transversals 3-2 – Angles and Parallel Lines 3-3 – Slopes of Lines 3-4 – Equations of lines 3-5 – Proving Lines Parallel 3-6 – Perpendiculars and Distance Chapter 4 – Congruent Triangles 4-1 – Classifying Triangles 4-2 – Angles of Triangles Triangle 4-3 – Congruent Figures Triangle 4-4 – Congruence by SSS and SAS 4-5 – Congruence by ASA and AAS 4-6 – Isosceles and Equilateral Triangles 4-8 – Triangles and Coordinate Proofs Chapter 5 – Relationships in Triangles 5-1 – Bisectors of Triangles 5-2 – Medians and Altitudes of Triangles 5-3 – Inequalities in One Triangle 5-4 – Indirect Proof Please study from your old tests/quizzes along with doing this packet for review. Your midterm consists of 2 sections; multiple choice and open-ended. This packet has a mixture of both types. IMPORTANT: TO STUDY FOR THIS MIDTERM, YOU SHOULD LOOK OVER ALL MATERIAL THAT HAS BEEN COVERED IN YOUR CLASS, SUCH AS HOMEWORK, ASSESSMENTS, AND NOTES. DO NOT ONLY STUDY FROM THIS PACKET!!! PACKET IS DUE THE DAY OF MIDTERM
LHA 059 (Peace River South) 28,885 Rural LHA 060 (Peace River North) 38,122 Rural LHA 057 (Prince George) 94,685 Urban/Rural Population (2015) Metro, Urban/Rural, Rural, Remote Vancouver Coastal Coastal Remote (LHA 83, 49) 4,269 Remote Coastal Rural (LHA 46-48) 87,431 Rural* Coastal Urban (LHA 44, 45) 193,190 Metro HSDA Richmond 208,148 Metro HSDA Vancouver 664,078 Metro Population (2015) Metro, Urban/Rural, Rural, Remote Vancouver Island Mt. Waddington 11,802 Rural LHA 064 Gulf Islands 15,454 Rural Alberni-Clayoquot 30,979 Rural Strathcona 44,960 Urban/Rural Comox Valley 65,356 Urban/Rural Cowichan Valley 83,264 Urban/Rural Nanaimo 154,827 Urban/Rural Capital Regional District 360,863 Metro Categorization based on population (0-10,000 = Remote; 10,001-40,000 = Rural; 40,001-190,000=Urban/Rural; 190,001+ = Metro) and geographical considerations (denoted with asterisk) 2015 Population: BC Stats, PEOPLE version 2015.
GEOGRAPHICAL PROTOCOLS FOR 2019 The following chart summarizes the geographical rotations and diversity profile for the 2019 continuing board members. (excerpts from each of the U.S. regional agreements are provided after the chart.) The chart also shows the states/countries for outgoing regional vice presidents. Aside from the West Coast protocol and the Texas and California dedicated seats, regional agreements say that no state may succeed itself unless there are no other qualified candidates in the eligible group and that nominations should give preference to a state that is not represented by the continuing VPs and that has not been represented recently. Regions: NE SE MW MP WC Intl Leadership Election year 2019 Outgoing VP PA SC MO (non-CEO position) AZ OR Netherlands Continuing Board CT, MA NC, VA IL, MN CO, TX CA, CA Canada, New Zealand CA, CO Population 63,317 29,083 33,662 222,209 74,486 62,787 30,166 39,462 144,186 64,403 98,780 128,800 23,549 98,889 Type of government if other than city F/AA/H 1AA 1F 1 F 1 F, 1 H, 1AS 1F 2 F Eligible states Group B other than VPs Southern Group other than VPs Non-CEO seat: any state other than VPs Group A: Other than VPs Group A: Other than VPs Northern Hemisphere Northeast At any given time, the “traditional” Northeast Vice Presidents on the ICMA Executive Board will represent different states within the region based on a North/South rotation. The “Non-CEO” Northeast Vice President will not be included in this rotation, but will be subject to the other provisions of this protocol. The Northern Tier will consist of the following states: Connecticut; Maine; Massachusetts; New Hampshire; Rhode Island; Vermont The Southern Tier will consist of the following states: Delaware; District of Columbia; Maryland; New Jersey; New York; Pennsylvania Vice Presidential positions shall be nominated according to the following rotation: Vice President Position #1 Selected from the northern tier Years to be Elected: 2014, 2017, 2020 Vice President Position #2 Selected from the southern tier Years to be Elected: 2013, 2016, 2019
The diagonals are perpendicular. ONE diagonal bisects the other. ONE diagonal bisects opposite angles. ONE pair of opposite congruent angles. The area of the kite is Fill-ins: 1) If all four sides of a kite have the same length (that is, if the kite is equilateral), it must be a _______________. 2) If a kite is , meaning that all four of its angles are equal, then it must also be equilateral and thus a _______________ Sample Test Questions: 1) 2) Assignment #3: Construct an equi-diagonal non-square, non-rhombus kite; that is a kite whose diagonals are equal in length, making sure the kite is not a square or rhombus. Assignment #4: Given that quadrilateral ABCD at the right is a kite: 1) Draw in diagonal AC. Label the intersection of the diagonals E. 2) Find _____ ______ _________ ________ 3) If AB = 6 and m<ABC = 60o, find: AC _____ BC ______ AE ______ CE _________ BE ______ 4) Describe a precise sequence of rigid motions that would show 5) Given the information from part 3 abo e, if DE = 6, find A) area of kite ABCD _____ AD ________ CD __________ perimeter of kite ABCD _______ If enough time: 1)
14 Community services 2 5 2 5 1 12 9 Trade 1 5 1 2 9 8 Health 2 1 4 1 6 Teaching 2 3 1 5 1 6 Small business 1 3 2 1 4 1 6 Arts 3 1 1 1 3 3 6 Office work 5 1 6 3 Beauty & fashion 1 1 1 3 2 Management 2 2 2 Armed Forces 1 1 2 2 Retail 1 1 2 Other: 1 Stock agent 1 1 1 Dairy farmer 1 1 1 Archaeology 1 1 1 Commerce 1 1 1 Civil engineering 1 1 2 Psychology 2 2 1 Business 1 1 *Notes: 1. Number of mentions not necessarily number of participants 2. Other: teaching – dance teacher skills developed through private classes throughout childhood; small business proposal for carpet cleaning no formal training proposed to be undertaken; armed forces recruitment and training processes; retail – informal on the job training; dairy farmer – taught by father throughout childhood. Table A2 Most popular career categories Number Career category 13 Community services 9 Trades 8 Health 6 Teaching 6 Office work 6 Arts 6 Small business owner Table A3 VET pathway preferred career categories Career category Career type No. of participants Community services Children’s services; youth work; aged care and disability 13 Trade Including pastry chef and chef; bricklaying; fabrication; electrician; civil construction; linesman; building or carpentry 9 Office work Local government; reception; other 6 Health Fitness; personal trainer; outdoor recreation 4 Beauty & fashion Make-up artist; beauty therapist 2 Management Hotel and local government 2
Example 3: a) Draw ΔJKL which has coordinates J(0,2), K(3,4), and L(5,1). b) Draw the image ΔJ’K’L’ after a reflection of ΔJKL over the x-axis. c) List the coordinates of J’K’L’. J (0, 2) J’ _________ K(3, 4) K’ _________ L(5, 1) L’__________ d) Draw the image ΔJ’’K’’L’’ after a reflection of ΔJ’K’L’ over the y-axis. e) List the coordinates of J’’K’’L’’. J’_________ J’’ _________ K’_________ K’’ _________ L’_________ L’’__________ f) Describe a different combination of two reflections that would move ΔJKL to ΔJ’’K’’L’’. g) Is this new image congruent or similar to the original figure? Example 4: a) Draw ΔABC which has coordinates A(0,1), B(3,4), and C(5,1). b) Draw the image ΔA’B’C’ after a reflection of ΔABC over x = -1. c) List the coordinates of A’B’C’. A (0, 1) A’ _________ B (3, 4) B’ _________ C(5, 1) C’__________
10) 11) Final Summary: Let’s go to to see some examples of dilations. If enough time: Let’s go to to help us summarize what we have learned in this lesson. Post If Enough Time: 1) 2)
A 60 B 54 C 36 D 18 44. ABCD is a parallelogram with diagonals intersecting at E. If AE = 3x + 12 and EC = 27, find the value of x. F 5 G 17 H 27 J 47 45. Find the values of x and y so that this quadrilateral is a parallelogram. A x = 13, y = 24 B x = 13, y = 6 C x = 7, y = 24 D x = 7, y = 6 46. Find the value of x so that this quadrilateral is a parallelogram. F 12 G 24 H 36 J 132 47. Parallelogram ABCD has vertices A(8, 2), B(6, –4), and C(–5, –4). Find the coordinates of D. A D(–5, 2) B D(–3, 2) C D(–2, 2) D D(–4, 8) 48. ABCD is a rectangle. If AC = 5x + 2 and BD = x + 22, find the value of x. F 5 G 6 H 11 J 26 49. Which of the following is true for all rectangles? A The diagonals are perpendicular. B The diagonals bisect the angles. C The consecutive sides are congruent. D The consecutive sides are perpendicular 50. ABCD is a rectangle with B(–4, 6), C(–4, 2), and D(10, 2). Find the coordinates of A. F A(6, 4) G A(10, 4) H A(2, 6) J A(10, 6) 51. For rhombus GHJK, find m∠1. A 22 B 44 C 68 D 90 52. The diagonals of square ABCD intersect at E. If AE = 2x + 6 and BD = 6x – 10, find AC.
70. Quadrilateral ABCD ∼ quadrilateral WXYZ, AB = 15, BC = 27, BC = 27, and the scale factor of WXYZ to ABCD is . Find XY. 71. The blueprint for a swimming pool is 8 inches by inches. The actual pool is 136 feet long. Find the width of the pool. 72. Find CD. 73. If quadrilateral ABCD ∼ quadrilateral PQRS, find BC. 74. △ABC ∼ △XYZ, AB = 12, AC = 16, BC = 20, and XZ = 24. Find the perimeter of △XYZ. For Questions 75 and 76, use the figure. 75. Identify the similar triangles. 76. Find the value of x. 77. The ratio of the measures of the three sides of a triangle is 3:4:6. If the perimeter is 91, find the length of the longest side.
86. Find the length of in ⨀R to the nearest hundredth. F 9.42 m G 4.71 m H 3.14 m J 1.57 m 87. Find YB if the diameter of ⨀A is 10 inches, the diameter of ⨀B is 8 inches, and AX = 3 inches. 88. Find the radius and diameter of a flying disc with a circumference of 11π inches. 89. In ⨀K, m∠HKG = x + 10 and m∠IKJ = 3x – 22. Find m . 90. The diameter of ⨀C is 18 units long. Find the length of an arc that has a measure of 100. Round to the nearest hundredth.
Problem 1: Nancy wrote a proof about the figure shown below. In the proof below, Nancy started with the fact that XZ is a perpendicular bisector of WY and proved that ∆WYZ is isosceles. Which of the following correctly replaces the question mark in Nancy’s proof? ASA SAA SAS SSS Answer: C Problem 2: Samuel wrote a proof about the figure below. In Samuel’s proof below he started with angle B being congruent to angle D and proved that ∆ABC is congruent to ∆EDC. It is given that angle B is congruent to angle D. By the converse of the Base Angle Theorem, AC is congruent to EC. By the Vertical Angle Theorem, angle BCA is congruent to angle DCE. ∆ABC is congruent to ∆EDC by the ? Congruence Theorem. Which of the following correctly replaces the question mark in Samuel’s proof? SSS AAS SAS ASA Answer: B Problem 3: Cui wrote a proof about the figure below.
Single attributes of 2D shapes and 3D objects sorting 2D shapes and 3D objects using a single attribute building and describing 3D objects (e.g., shaped like a can) Grade 1 Comparison of 2D shapes and 3D objects sorting 3D objects and 2D shapes using one attribute, and explaining the sorting rule (Activities 7–10) Cross Strand: Repeating patterns with multiple elements and attributes identifying sorting rules (Activities 9, 10) Grade 2 Multiple attributes of 2D shapes and 3D objects sorting 2D shapes and 3D objects using two attributes, and explaining the sorting rule identifying 2D shapes as part of 3D objects Curriculum Correlation Geometry Cluster 2: 3-D Solids SK Kindergarten Shape and Space SSK.2 Sort 3-D objects using a single attribute. SSK.3 Build and describe 3-D objects. Grade 1 Shape and Space SS1.2 Sort 3-D objects and 2-D shapes using one attribute, and explain the sorting rule. (Activities 7–10) Grade 2 Shape and Space SS2.3 Describe, compare, and construct 3-D objects, including: • cubes • spheres • cones • cylinders • pyramids. SS2.5 Demonstrate understanding of the relationship between 2-D shapes and 3-D objects.
Sorting Solids Behaviours/Strategies Student is unable to select a solid based on the needed attribute. Student focuses on one shape and doesn’t realize that more than one shape can be a face of a solid. Student identifies some faces but doesn’t rotate the solid to see the different faces (shapes). Observations/Documentation Student recognizes some shapes but doesn’t recognize a shape when it doesn’t match her or his mental image of the shape. Student can only sort a solid in one way. Student can sort solids with ease. Observations/Documentation
B. a rectangle with a length of 20 units and a width of 10 units C. a rectangle with a length of 10 units and a width of 7 units D. square with side lengths of 20 units 10.) If the cube shown below is sliced by a plane through vertices 1, 2, 7, and 8, which of the following best describes the cross-section of the cube? 11.) Abbey is getting new carpet in her living room and hallway. The following diagram shows the two together. If a = 36 ft, b = 14 ft, c = 18 ft, and d = 18 ft, what is the area of the living room and hallway together? Note: Figure not drawn to scale 12.) If X = 2 inches, Y = 10 inches, W = 4 inches, and Z = 5 inches, what is the area and perimeter of the object? Area = Perimeter =
Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. basis for modeling situations geometrically Essential Question(s) How can information, definitions, postulate, properties and theorems helpful in writing proofs? Objective(s): Students will use algebra to write two – column proofs. Students will use properties of equality to write geometric proofs. proof Writing in Math Compare and contrast informal or paragraph proofs with formal or two-column proofs. Which type of proof do you find easier to write? Justify your answer. Transformations and Congruence; Transformations and Symmetry (Allow approximately 3 weeks for instruction, review, and assessment) Domain: Cluster: Understand congruence in terms of rigid motion Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. Enduring Understanding(s) Proving and applying congruence provides a basis for modeling situations geometrically Essential Question(s) How do you identify corresponding parts of congruent triangles? How do you show that two triangles are congruent? Objective(s): Students will identify corresponding sides and corresponding triangles of congruent triangles. Students will explain that in a pair of Lesson 4.3 – Congruent Triangles, pp. 253 – 261 (Lesson 1.2 in document) Use the following resources to ensure that the intended outcome and level of rigor of the standards are met. Task(s) TN Geometry Instructional Task- Comparing Shapes Vocabulary Congruent, congruent polygons, corresponding parts Writing in Math Determine whether the following statement is always, sometimes, or never true. Explain your reasoning. Equilateral triangles are congruent.
ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. ability to apply that knowledge to problems. Domain: Cluster: Apply geometric concepts in modeling situations Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). ★ Enduring Understanding(s) Geometric figures can change size and/or position while maintaining proportional attributes. Essential Question(s) How do you use proportions to find side lengths in similar polygons? Objective(s): Interpret scale models Use scale factors to solve problems Use the following lesson(s) first to introduce concepts/build conceptual understanding. Use the textbook resources to address procedural skill and fluency. Lesson 7.7 Scale Drawings and Scale Models pp. 512-517 Vocabulary Scale model, scale drawing, scale Writing in Math/Discussion Compare and contrast scale and scale factor. You can produce a scale model of a certain object by extending each dimension by a constant. What must be true of the shape of the object? Explain your reasoning. Using Similar Triangles (Allow approximately 3 weeks for instruction, review, and assessment) Domain: Cluster: Prove theorems involving similarity Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity. Domain: Cluster: Prove theorems involving similarity Use congruence and similarity criteria for triangles to solve problems and to Enduring Understanding(s) Polygons are similar if and only if corresponding angles are congruent and corresponding sides are proportional. Essential Question(s) How do you use proportions to find side lengths in similar polygons? How do you show two triangles are similar? Objective(s): Identify and prove similar triangles Use the following lesson(s) first to introduce concepts/build conceptual understanding. Use the textbook resources to address procedural skill and fluency. Lesson 7.3 Similar Triangles pp. 474-483 Writing in Math/Discussion Contrast and compare the triangle congruence theorems with the triangle similarity theorems.
Geometry UNIT 2 Unit 2: Geometric Angle Theorems 2.1 Angle Relationships G.2.A, G.2.B, G.2.D I can correctly identify the relationship between pairs of angles formed by intersecting lines, both parallel and perpendicular, pairs of lines. This means I can Identify complementary, supplementary, alternate interior/exterior, same-side interior/exterior and corresponding angle pairs Calculate the measure of angles given one or two angles on a diagram using the angle relationships identified above Know, prove and apply theorems about parallel and perpendicular lines. 2.2 Triangle Angle Relationships G.3.A I can correctly identify the relationship between angles formed inside a triangle. This means I can Use the Triangle Angle Sum Theorem to find missing angles in a triangle Know and apply basic postulates and theorems about triangles and special lines, line segments, and rays associated with triangles 9/24 Notes on Angle Relationships P74/2-3, 5, 18, 20 25 Notes on Angles formed by lines & a transversal P80/2-16, 17, 31, 32 26 Final Review for Unit 1 Test 27 Standard 2.1 WS Angle Pair Relationships 28 Unit 1 Test on Conditional Statements & Transformations 10/1 Standard 2.1 P91/2-37, 38, 45 10/2 Notes on Standard 2.2 Triangle Angle Sum & Inequality P100/2-62 to 2-64 10/3 (ER) Standard 2.1 WS Rally Coach Angle Pairs 10/4 Standard 2.1 & 2.2 WS Standard 2.1 & 2.2 Work P97/2-51 & 2-52 10/5 Standard 2.1 & 2.2 WS Rally Coach Angle & Triangle Relationships 8 Take-Home Practice Test on 2.1 & 2.2 9 10 11 12 Unit 2 Test on Geometric Angle Relationships
Right angle Right triangle Rigid transformation rotation Rotational symmetry Sample space scalar Scale factor Scalene triangle secant Secant segment Sector of a circle segment Segment bisector Segment of a circle semicircle Semi-regular tessellation Sides of an angle Sierpinski Triangle Similarity ratio simulation sine Skew lines Slant height slope Slope-intercept form space sphere Spherical geometry square Standard position statement Supplementary angles Surface area symmetry tangent Tangent segment tessellation theorem Topographic map transformation translation Translation vector transversal Tree diagram Trigonometric ratio trigonometry Truth table Two-column proof Two-stage experiment Undefined term Uniform tessellations vector Vertex of an angle Vertical angles volume
429 in2 1350 m2 87 m2 517.5 yd2 819 ft2 126 ft 360 ft2 185 cm2 486 yd2 702 yd2 288 in2 1012 yd2 90 ft2 560 yd2 558 in2 118 in 2 m3 ft3 4 ft cm3 1 m3 5 cm3 in3 5 m3 m3 ft3 3 ft cm3 14 m3 ft3 mm3 m3 Add the area of each face to find the total surface area. 2(70)+2(140)+2(98)= 616in2 13,642.5 in3 The problem says "approximately" to account for the unavailable space inside the tub. 32x18x59.5=34,272 in2 71.5 cm2 108in3 Add the area of each face to find the total surface area. 2(36) + 4(18)=144 in2
14 units 24 units2 24 units2 obtuse, isosceles triangle See map see map 36 sq units isosceles, right triangle see map (5x8.5)-(6+12.75+6.25)=42.5-25=17.5u2 Cutler, Dixon and Reading. P=2(2) + (2)4) = 12 units Geometry Unit Review Multiple Choice Question Answers b c c d b c d c b d c b d b c c Geometry Unit Review Short Constructed Response Answers 12 m 8 sheets of paper 397 ft2 104 m2 1 box, 302 in2 more 11424 in2 8 drapes 4 in3 18 units2
13. ABCD is a quadrilateral. What is the value of a? Open-Response 1. Parallel Illusions Often lines that luuk parallel are not parallel. Which two lines in the diagram below are parallel? Justify your answer. 2. Deck Boards Sonya is building a rectangular deck in her backyard. The deck will have support beans running through the center, making 4 isosceles triangles, as shown below. Determine the values of x and y. Justify your answers. 3. What’s Missing? Consider the following diagram and complete the table below. Justify your answers.
Show that the volume of the solid created by revolving a -- triangle about its hypotenuse is . A Progression Toward Mastery Assessment Task Item STEP 1 Missing or incorrect answer and little evidence of reasoning or application of mathematics to solve the problem. STEP 2 Missing or incorrect answer but evidence of some reasoning or application of mathematics to solve the problem. STEP 3 A correct answer with some evidence of reasoning or application of mathematics to solve the problem, OR an incorrect answer with substantial evidence of solid reasoning or application of mathematics to solve the problem. STEP 4 A correct answer supported by substantial evidence of solid reasoning or application of mathematics to solve the problem.
b G-GMD.B.4 Student identifies the shape as a triangle or other two-dimensional figure or left the item blank. Student misidentifies the shape formed but correctly states it as a three-dimensional solid. Student concludes that the shape formed by the revolution is a right circular cone or cone. Student provides a complete sentence identifying the solid formed as a right circular cone or cone. c G-GMD.B.4 Student provides incorrect answers for both solids, and it is not evident that formulas were used. Student used the correct formulas for volume but makes computational errors leading to incorrect volumes for both solids. Student correctly calculates the volume of one of the solids but may have made a computational error leading to an incorrect volume for the second solid. Student correctly provides the volume of both solids (i.e., and ). d G-GMD.B.4 Student made little or no attempt to answer the question. Student provides a solution with the correct steps but makes one conceptual error leading to an incorrect answer, such as using an incorrect formula. Student provides a solution with the correct steps but makes one computational error leading to an incorrect answer. Student correctly identifies the volume as and includes a complete solution. Name Date State the volume formula for a cylinder. Explain why the volume formula works. The volume formula for a pyramid is , where is the area of the base and is the height of the solid. Explain where the comes from in the formula. Give an explanation of how to use the volume formula of a pyramid to show that the volume
mm Find the area of mm2 Find the perimeter of quadrilateral . mm In circle , and . Find The radius of the circle. (round to the nearest whole number) Closing (3 minutes) Project the picture to the right. Have students do a 30 second quick write on all they know about the diagram if: is tangent to the circle at point . is tangent to the circle at point . is tangent to the circle at point . Then have the class as a whole share their ideas. , ,
In right triangle KLM, . Let . What is ? Explain your answer. 4. Answer ONE of the following: a. Explain why angle- angle is enough to establish similarity between two triangles. OR b. Explain why congruence is a special case of similarity. Answers to Geometry Midterm D C B C C & F C A B C C C B D D D Part A: A Part B: C D B segments AB & CD 110 feet Statements Reasons 1. 1. C. Given 2. 2. A. If 2 parallel lines are cut by a transversal, then the alternate interior angles are congruent. 3. 3. D. Vertical Angles are congruent 4. 4. E. AA~
Geometry Parking Lot Poster Rubric 4 3 2 1 Poster Design Poster uses color, includes picture of final design, a close-up of a set of parallel and perpendicular lines, is well organized, uses mathematical vocabulary, and incorporates creative elements. Poster includes picture of final design, a close-up of a set of parallel and perpendicular lines is organized, uses some math vocabulary, but is not creative or colorful. Poster includes picture of final design, but lacks a close-up of parallel and perpendicular lines, is disorganized, and uses little math vocabulary. Poster has no picture of final design, is missing information, and shows significant lack of effort. Math content Poster shows two examples of parallel lines and one example of perpendicular lines using proof and geometric theorems. Poster shows one example of parallel and one example of perpendicular lines using proof and geometric theorems. Poster mentions parallel or perpendicular lines, but contains no theorems or proofs. Poster does not mention parallel or perpendicular lines. Extra content Parking lot design clearly fits all constraints provided and lists costs and sources for any research. Parking lot design fits most constraints, lists costs and sources for any research. Parking lot design fits some constraints, lists either costs or resources. Parking lot design fits none of the constraints, does not list cost or sources for research. Justification Poster includes mathematical, aesthetic, and legal justification for design choices. Poster includes some justification for design choices, using math at least. Poster includes little justification for design choices, not including math. Poster includes no justification for design choices. Peer critique Peers give high marks for your poster. Peers give mixed results for your poster. Peers give generally low marks for your poster. Peers give consistently low marks for your poster.
Prism Polyhedron BA(H) Sum of all lateral faces (For a right prism, it is (Pbasex Heightprism) Sum of all bases/faces Pyramid Polyhedron 1/3 (BH) 1/2 (PS) (perimeter of base x slant height) /2 BA + (LA) (base area + lateral area) Cylinder Non-Polyhedron πR2(h) 2 πR(h) 2 πR(h) + 2(πR2) Cone Non-Polyhedron 1/3 πR2 (h) πSR πR2+LA Sphere Non-Polyhedron 4/3 ( πR3) n/a 4 πR2 Euler’s Law: (for any polyhedron) (Faces+vertices)-edges=2 Regular polyhedra (platonic solids) A regular polyhedron is a polyhedron whose faces are congruent, regular polygons, and that has the same number of faces intersecting at each vertex. Trig ratios SOH-CAH-TOA Area of regular polygons ASN (apothem x side length x number of sides) 2 Coordinate Geometry FORMULAS FOR LINE SEGMENTS Midpoint= M= _____________________________________________________________________________________ Distance=
5. 2 – 3x – 2 6. 16 – 8r + 1 7. 6 + 5x – 6 8. 3 + 2x – 8 Examples: Solve the equation by factoring and then use the Zero-Product property. Show all work 3. 4 + 27x – 7 = 0 4. 3 + 29x – 10 = 0 5. 6 – 5x – 4 = 0
STAGE III: LEARNING PLAN INSTRUCTIONAL PROCEDURES: (Active Engagement, Explicit Instruction, Metacognition, Modeling, Scaffolding) DAILY: Warm up to include spiraling review of prior knowledge to include upcoming lesson DAILY: Check for understanding using warm up, homework, exit slips, or formative assessment questioning to determine whether to continue lesson or do interventions as needed. (model, spiral scaffolding, instruct/ reteach as needed) MINI LESSON: Based on daily assessments (formative and summative), additional modeling, instruction, homework, review, interventions, group work, computer or teacher guided practice will be done. MATERIALS AND RESOURCES: Unit 1 Points, Lines, and Planes (Glencoe Geometry text) Summer Skills review & test Warm ups (daily) Homework (daily) “Grab & Go” worksheets/ activities Unit Test Additional materials as needed (rulers, compass, grid paper, etc) INTERVENTIONS: Skills Tutor Math Lab Study Island Keystone Classroom Diagnostic Tool Small group/flexible grouping will occur. ASSIGNMENTS: p 9-10#13-22, 25-27, 30-46 Skills Practice: pp. 1-6 ( Points , Lines & Planes) p 17 #12-15, 22-27 p 17-19#28-39, 58, 62 Skills Practice: pp. 7-12 (Measuring Line Segments) p 25# 13-30 p 26 #31-42 Skills Practice: pp. 13-18( Distance Between Two Points) p 33-34 #4-6, 12-24 p 34 #25-33 p 34 #34-39, 52-61, 63, 65 Skills Practice: pp. 19-24( Measuring Angles) p 42 #11-25 (skip #17) study guide & intervention 1.5 p 42 #17, 27-35, 37 Skills Practice: pp. 25-30( Pairs of Angles) p 49-50 #12-25, 29-34 p49-50 #26-28 Skills Practice: pp. 31-36( Polygons) review test Supplemental\ Adaptive Materials Completed
ASE MA 04: Geometry, Probability, and Statistics Steve Schmidt schmidtsj@appstate.edu abspd.appstate.edu Overview This workshop will assist instructors in teaching geometry, probability and statistics so their learners will have the skills and knowledge to be successful on equivalency exams and in transitioning to college and careers. Agenda 8:30 – 10:00 Geometry 10:00 – 10:15 Break 10:15 – 11:45 Geometry 11:45 – 12:45 Lunch 12:45 – 2:00 Statistics/Data Analysis 2:00 – 2:15 Break 2:15 – 4:00 Is There a Math Brain? Please Write on this Packet! You can find everything from this workshop at: abspd.appstate.edu Look under: Teaching Resources, Adult Secondary Resources, Math
Geometry Honors Chapter 11 Schedule - Hronek Summer 2018 Day Date Topic # HW W 7/11 R Review 37 Pg 709 #7-28 W 7/11 R Review 38 Pg 712 #1-19 W 7/11 T Test Chap 10 39 Pg713 #1-24 W 7/11 11.1 Area and Perimeter formulas for Triangles and Parallelograms 40 Pg.723 #3-8, 16-20, 22-27, 32-33 W 7/11 11.2 Area and Perimeter formulas for Trapezoid, Rhombus and Kite 41 Pg.733 #7-29 W 7/11 11.3 Perimeter and Area of Similar Figures 42 Pg 740 # 3, 4, 7-10, 14, 16-20, 24, 25, 31, 34, 39-41 Th 7/12 11.5 Area of Circles and Sectors 43 Pg 758 # 13, 16-19, 26, 28, 30, 31, 33, 35, 36, 42, 43, 44 Th 7/12 11.6 Areas of Regular Polygons 44 Pg 765 #14-16,18-21, 27-35, 47, 48 Th 7/12 R Review 45 Pg.916 #2-48 even Pg 778 # 1-6 Th 7/12 11.7 Geometric Probability 46 Pg 774 # 3-6, 8-10, 16-27, 30 Quiz # 1-4 Th 7/12 R Review 47 Review Worksheet 1 Th 7/12 R Review 48 Review Worksheet 2 M 7/16 Review 49 Pg.780 #5-26 M 7/16 Review 50 Pg.784 #1-19 M 7/16 T Chapter 11 Test 51 Pg.785 #1-7
dodecahedron edge (of polyhedron) Equator face (of polyhedron) frustum (of cone or pyramid) geodesic great circle height (of prism, pyramid, cylinder or cone) hemisphere hexahedron inscribed (prism or pyramid) icosahedron isometric drawing lateral surface latitude longitude meridian net non-convex octahedron Platonic solid polyhedron Prime Meridian prism pyramid projection regular polyhedron semi-regular polyhedron Schläfli symbols Schlegel diagram semi-regular polyhedron slant height solids generated by rotations of plane figures sphere spherical coordinates spherical excess spherical triangle surface area surface of revolution tesseract tetrahedron three-dimensional figure trilateration vertex (of polyhedron) volume Assessments Mid-Unit Performance Task – Students construct to mobiles, one of equal surface area polyhedra and one that uses the same polyhedra and are filled with materials. Other Evidence (Formative and Summative Assessments) • Exit slips • Class work • Homework assignments • Math journals • Mid-unit Performance Task • End-of-unit test