Unit 4 Triangle Congruence Week 10 – to Theorems 49 CCSS.MATH.CONTENT.HSG.CO.B.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. Come up with a conclusion as a result: Successive reflection in two intersecting mirror lines produces a rotation about the point of intersection through twice the angle between the mirror lines. Successive reflection in parallel mirror lines produces a translation in a direction perpendicular to the mirrors through a distance equal to twice the distance between the mirrors Any rigid motion of the Euclidean plane can be written as a composition of no more than 3 reflections. I can explain how and why; Successive reflection in two intersecting mirror lines produces a rotation about the point of intersection through twice the angle between the mirror lines. Successive reflection in parallel mirror lines produces a translation in a direction perpendicular to the mirrors through a distance equal to twice the distance between the mirrors and Any rigid motion of the Euclidean plane can be written as a composition of no more than 3 reflections. Unit 4 Triangle Congruence Week 10 – to Theorems 50 Assessment Assessment Assessment Unit 4 Triangle Congruence Week 11 – Proofs of Congruent Triangles 51 CCSS.MATH.CONTENT.HSG.CO.B.7 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. Identifying Congruent sides of a triangle I can Identify congruent sides of a triangle
Unit 4 Triangle Congruence Week 12 – Congruent Parts of Congruent Figures are Congruent 57 CCSS.MATH.CONTENT.HSG.CO.B.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. Use the postulate ASA to show that triangles are congruent. Also apply it so solve other geometric problems. Use the postulate ASA to show that triangles are congruent. Also apply it so solve other geometric problems. Unit 4 Triangle Congruence Week 12 – Congruent Parts of Congruent Figures are Congruent 58 CCSS.MATH.CONTENT.HSG.CO.B.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. Use the postulate SAS to show that triangles are congruent. Also apply it so solve other geometric problems. I can use the postulate SAS to show that triangles are congruent. I can apply the postulate to solve other geometric problems. Unit 4 Triangle Congruence Week 12 – Congruent Parts of Congruent Figures are Congruent 59 CCSS.MATH.CONTENT.HSG.CO.B.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. Use the postulates SSS, SAS and ASA to show that triangles are congruent. Also apply them to solve other geometric problems. I can use the postulates SSS, SAS and ASA to show that triangles are congruent and also apply them to solve other geometric problems. Unit 4 Triangle Congruence Week 12 – Congruent Parts of Congruent Figures are Congruent 60 Assessment Assessment Assessment
Geometry Unit 4 Skills List Number Unit CCSS Skill 15 4 HSG.CO.B.6 Describing transformation theorems 16 4 HSG.CO.B.7 Showing congruence in triangles 17 4 HSG.CO.B.8 Explain the criteria for triangle congruence
Unit: Unit 4 Triangle Congruence Course: Geometry Topic: Week 10 – Transformations to Theorems Day: 47 Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.B.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. Mathematical Practice: CCSS.MATH.PRACTICE.MP4 Model with mathematics. CCSS.MATH.PRACTICE.MP5 Use apprpriate tools strategically. CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others. Objective: Come up with a result(conclusion) as a result: Any plane rigid motion is invertible. Any rigid motion with a fixed point is either a reflection or a rotation I can statement: I can explain how and why: Any plane rigid motion is invertible. Any rigid motion with a fixed point is either a reflection or a rotation Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 4. They will illustrate the fixed points of an pre-images under rotation 3. The presentation will be used to look for misconceptions and encourage discussion. Materials: Bellringer 47 Day 47 Activities Day 47 Practice Day 47 Presentation Day 47 Exit Slip
Unit: Unit 4 Triangle Congruence Course: Geometry Topic: Week 10 – Transformations to Theorems Day: 48 Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.B.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. Mathematical Practice: CCSS.MATH.PRACTICE.MP4 Model with mathematics. CCSS.MATH.PRACTICE.MP5 Use apprpriate tools strategically. CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others. Objective: Come up with a conclusion as a result: The composition of two rigid motions is also a rigid motion The composition of a half-turn and a reflection is a glide reflection. I can statement: I can explain howand why: The composition of two rigid motions is also a rigid motion The composition of a and a reflection is a glide reflection. Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of three to discover that the composition of two rigid motions is also a rigid motion Materials: Bellringer 48 Day 48 Activities Day 48 Practice Day 48 Presentation Day 48 Exit Slip turn
Unit: Unit 4 Triangle Congruence Course: Geometry Topic: Week 10 – Transformations to Theorems Day: 50 Common Core State Standard: Assessment Mathematical Practice: Assessment Objective: Assessment I can statement: Assessment Procedures: Assessment Materials: Assessment Accommodations/Special Circumstances: Technology: Reflection: Extra/Additional Resources:
Unit: Unit 4 Triangle Congruence Course: Geometry Topic: Week 11 – Proofs of Congruent Triangles Day: 52 Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.B.7 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. Mathematical Practice: CCSS.MATH.PRACTICE.MP2 Reason abstractly and quatitatively. Objective: Identifying Congruent angles of a triangle I can statement: I can Identifying congruent angles of a triangle Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of four to identify congruent angles in congruent triangles 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day. Materials: Bellringer 52 Day 52 Activities Day 52 Practice Day 52 Presentation Day 52 Exit Slip Accommodations/Special Circumstances: Technology:
Unit: Unit 4 Triangle Congruence Course: Geometry Topic: Week 11 – Proofs of Congruent Triangles Day: 53 Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.B.7 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. Mathematical Practice: CCSS.MATH.PRACTICE.MP2 Reason abstractly and quatitatively. CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them. Objective: 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. I can statement: I can 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. Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 5. They like show that if two triangles are congruent, then they have corresponding angles and sides. 3. The presentation will be used to look for misconceptions and encourage discussion. Materials: Bellringer 53 Day 53 Activities Day 53 Practice Day 53 Presentation Day 53 Exit Slip
Unit: Unit 4 Triangle Congruence Course: Geometry Topic: Week 11 – Proofs of Congruent Triangles Day: 54 Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.B.7 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. Mathematical Practice: CCSS.MATH.PRACTICE.MP7 Look for and make use of structure. Objective: Show Congrence of image and object distance in dilation if scale factor is -1. I can statement: I can show congrence of image and object distance in dilation if the scale factor is Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. They will draw a triangle and its image under a dilation with a scale factor of -1 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day. Materials: Bellringer 54 Day 54 Activities Day 54 Practice Day 54 Presentation Day 54 Exit Slip -
Accommodations/Special Circumstances: Technology: Reflection: Extra/Additional Resources: Unit: Unit 4 Triangle Congruence Course: Geometry Topic: Week 11 – Proofs of Congruent Triangles Day: 55 Common Core State Standard: Assessment Mathematical Practice: Assessment Objective: Assessment I can statement: Assessment Procedures: Materials:
Assessment Assessment Accommodations/Special Circumstances: Technology: Reflection: Extra/Additional Resources: Unit: Unit 4 Triangle Congruence Course: Geometry Topic: Week 13 – Rigid Motion – Putting it all together Day: 61 Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.B.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. Mathematical Practice: CCSS.MATH.PRACTICE.MP2 Reason abstractly and quatitatively. CCSS.MATH.PRACTICE.MP7 Look for and make use of structure.
Accommodations/Special Circumstances: Technology: Reflection: Extra/Additional Resources: Unit: Unit 4 Triangle Congruence Course: Geometry Topic: Week 13 – Rigid Motion – Putting it all together Day: 65 Common Core State Standard: Assessment Mathematical Practice: Assessment Objective: Assessment I can statement: Assessment Procedures: Materials:
a. Identify four rigid motions b. Identify those that preserves orientations and those that do not. c. Identify those that have fixed point(s) and those that do not. An geometric figure is reflected about then rotated by about Compare the sizes of the two images Comment on the orientation of the two images Compare the interior angles of the images. Identify all fixed point on the figure ABCD id reflected about line M. Week 10 - Keys Weekly Assessments
a. Identify four rigid motions Rotation Translation Refection Glide reflection b. Identify those that preserves orientations and those that do not. Translation c. Identify those that have fixed point(s) and those that do not. Rotation Reflection Glide reflection An geometric figure is reflected about then rotated by about Compare the sizes of the two images They have the same size Comment on the orientation of the two images They have different orientations Compare the interior angles of the images. The corresponding angles are equal Identify all fixed point on the figure ABCD id reflected about line M. Fixed points are points that will not move after the transformation. These are all points on ABCD that lie on M.
4. Identify all pairs of congruent angles. 5. Basing on questions 1-4 above, what do you conclude about the two triangles? The figure below shows two triangles. has been mapped to after a translation. Study it and use it to answer questions 6-10. 6. Identify all pairs of corresponding sides. 7. Identify all pairs of corresponding angles. 8. Identify all pairs of congruent angles. 9. Show the mapping of corresponding vertices. 10. What can you say about the sizes and the shapes of the two triangles with reference to each other?
Answer keys Day 52: 1. KL and PQ LM and QR KM and PR 2. and and and 3. 4. and and and 5. The two triangles are congruent. 6. AB and PR BC and RQ AC and PQ 7. and and and 8. and and and 9. 10. They have the same size and shape. 11. AB and PQ BC and QR AC and PR 12. and and and 13. and and and 14. 15. Yes. Rigid motion preserves distances. 16. PQ and XZ QR and ZY PR and XY
Weekly Assessments Week #11 KEY Use the triangles below to answer the questions that follow Which rigid motion will map the two triangle onto each other? Reflection What is the size of What is the size of Is Yes Construct squares inscribed in each circle below. a) A circle with a radius of b) A circle with a radius of.
15. What is the value of a? 16. What is the value of ? 17. Find the value of c? From question 18 - 20, state the postulate which makes each pair of triangles congruent. 18. 19. 20.