Cluster: Understand congruence in terms of show that two triangles are congruent by understanding. If used, these lessons should be used before the lessons from the textbooks. rigid motions SSS or SAS. Additional Lesson(s): Explain how the criteria for triangle Engageny Geometry Module 1, Topic D, congruence (ASA, SAS, and SSS) Lesson 22 – Triangle Congruence follow from the definition of congruence in terms of rigid motions. Proving properties of Geometric Figures, students use what they have learned in Topics Domain: A through C to prove properties(Students Cluster: Make geometric constructions learn why any two triangles that satisfy the SAS congruence criter. Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle Domain: Enduring Understanding(s) Lesson 4.5 Proving Triangles Congruent – ASA, Vocabulary Cluster: Prove theorems involving similarity AAS. Pp.273-280 There exist methods for proving triangles Included side congruent. Lesson 4.5 ext Congruence in Right Triangles Use congruence and similarity criteria p.281-282 for triangles to solve problems and to Writing in Math prove relationships in geometric Choose from the following resources to Essential Question(s) Explain why identifying two pairs of congruent figures. ensure that the intended outcome and level What does the ASA Triangle Congruence angles with their included sides congruent is of rigor (mainly conceptual understanding Domain: Theorem tell you about triangles? enough to prove that two triangles are and application) of the standards are met. Cluster: Understand congruence in terms of congruent. What does the AAS Triangle Congruence rigid motions Task(s) Theorem tell you about triangles? Select appropriate tasks from Use the definition of congruence in What does the HL Triangle Congruence terms of rigid motions to show that two Theorem tell you about two triangles? triangles are congruent if and only if corresponding pairs of sides and Objective(s): corresponding pairs of angles are congruent. Students will use the ASA Postulate to test for triangle congruence. Domain: Students will use the AAS Postulate to Cluster: Understand congruence in terms of test for triangle congruence. rigid motions Students will explore congruence in right Explain how the criteria for triangle triangles. congruence (ASA, SAS, and SSS)
Cluster: Understand congruence in terms of rigid motions Explain how the criteria for triangle congruence (ASA, SAS, and SSS) 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 show that two triangles are congruent by SSS or SAS. understanding. If used, these lessons should be used before the lessons from the textbooks. Additional Lesson(s): Engageny Geometry Module 1, Topic D, Lesson 22 – Triangle Congruence Proving properties of Geometric Figures, students use what they have learned in Topics A through C to prove properties(Students learn why any two triangles that satisfy the SAS congruence criter. Domain: Cluster: Prove theorems involving similarity Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Domain: Cluster: Understand congruence in terms of rigid motions 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. Domain: Cluster: Understand congruence in terms of rigid motions Explain how the criteria for triangle congruence (ASA, SAS, and SSS) Enduring Understanding(s) There exist methods for proving triangles congruent. Essential Question(s) What does the ASA Triangle Congruence Theorem tell you about triangles? What does the AAS Triangle Congruence Theorem tell you about triangles? What does the HL Triangle Congruence Theorem tell you about two triangles? Objective(s): Students will use the ASA Postulate to test for triangle congruence. Students will use the AAS Postulate to test for triangle congruence. Students will explore congruence in right triangles. Lesson 4.5 Proving Triangles Congruent – ASA, AAS. Pp.273-280 Lesson 4.5 ext Congruence in Right Triangles p.281-282 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 Vocabulary Included side Writing in Math Explain why identifying two pairs of congruent angles with their included sides congruent is enough to prove that two triangles are congruent.