follow from the definition of congruence in terms of rigid motions. Domain: Cluster: Make geometric constructions Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle Students will write formal proofs to show that two triangles are congruent by AAS, ASA or HL. Domain: Cluster: Prove geometric theorems Prove theorems about triangles. Domain: Cluster: Make geometric constructions Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Domain: Cluster: Prove theorems involving similarity Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Enduring Understanding(s) Many relationships exist between the measure of the angles of a triangle and the measure of the sides of the triangle. Essential Question(s) What are the special relationships among angles and sides in isosceles and equilateral triangles? Objective(s): Students will use properties of isosceles triangles. Students will use properties of equilateral triangles. Students will prove base angles of isosceles triangles are congruent. Lesson 4.6 Isosceles and Equilateral Triangles, pp. 283-291 Choose from the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met. Use the following Engageny Lessons to introduce the concepts/build conceptual understanding. If used, these lessons should be used before the lessons from the textbooks. Additional Lesson(s): Engageny Geometry Module 1, Topic D, Lesson 23 – Isosceles Triangles Vocabulary Pythagorean triple Writing in Math p. 290 #45 Challenge – proof (H.O.T. problem) Special Segments in Triangles (Allow 2.5 weeks for instruction, review, and assessment) Domain: Cluster: Prove geometric theorems Prove theorems about triangles. Enduring Understanding(s) The properties of triangles create a basis for understanding and reasoning that extends to Lesson 5.1 Bisectors of Triangles pp. 321-331 Choose from the following resources to Vocabulary Perpendicular bisector, concurrent lines, point of concurrency, circumcenter,
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). ★ other geometric figures. Essential Question(s) How can you use perpendicular bisectors to find the point that is equidistant from all the vertices of a triangle? How can you use angle bisectors to find the point that is equidistant from all the sides of a triangle? Objective(s): Students will identify and use perpendicular bisectors in triangles Students will identify and use angle bisectors in triangles. Students will construct the special segments (perpendicular bisectors and angle bisectors) in acute, right and obtuse triangles. Students will prove the perpendicular bisectors and the angle bisectors of a triangle meet at a point. ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met. Task(s) Centers of Triangles Centers of Triangles Solutions Geometry Lab - Constructing Bisectors p. 321 incenter Writing in Math Compare and contrast the perpendicular bisectors and angle bisectors of a triangle. Be sure to include their points of concurrency. Why are the points of concurrency called incenter for angle bisectors of triangles and circumcenter for the perpendicular bisectors? 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) The properties of triangles create a basis for understanding and reasoning that extends to other geometric figures. Essential Question(s) How can you find the balance point or center of gravity of a triangle? Lesson 5.2 Medians and Altitudes of Triangles pp. 332-341 Use the following Engageny Lessons to introduce the concepts/build conceptual understanding. If used, these lessons should be used before the lessons from the textbooks. Additional Lesson(s): Engageny Geometry Module 1, Topic E, Lesson 30 – Vocabulary Median, centroid, altitude, orthocenter Writing in Math Summarize the special segments of a triangle including their names, properties and diagrams into a chart or booklet.
be used before the lessons from the textbooks. Additional Lesson(s): Engageny Geometry Module 1, Topic E, Lesson 28 – Domain: Cluster: Prove geometric theorems Prove theorems about parallelograms. Domain: Cluster: Use coordinates to prove simple geometric theorems algebraically Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, 3) lies on the circle centered at the origin and containing the point (0, 2). Enduring Understanding(s) The properties of quadrilaterals help you to categorize quadrilaterals Essential Question(s) What criteria can you use to prove that a quadrilateral is a parallelogram? Objective(s): Students will recognize the conditions that ensure a quadrilateral is a parallelogram. Students will prove that a set of points forms a parallelogram in the coordinate plane. Lesson 6.3 Tests for Parallelograms pp.409-417 Choose from the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met. Task(s) Select appropriate tasks from Graphing Technology Lab - Parallelograms p. 408 Whitebeard's Treasure Task TN Task: Park City Use the following Engageny Lessons to introduce the concepts/build conceptual understanding. If used, these lessons should be used before the lessons from the textbooks. Additional Lesson(s): Engageny Geometry Module 4, Topic D, Lesson 13 – Writing in Math Journal Question: Are two parallelograms congruent if they both have four congruent angles? Justify your answer Domain: Cluster: Prove geometric theorems Enduring Understanding(s) The properties of quadrilaterals help you to categorize quadrilaterals Lesson 6.4 Rectangles Lesson 6.5 Rhombi and Squares Vocabulary rectangle, rhombi, and square.