follow from the definition of congruence Students will write formal proofs to show in terms of rigid motions. that two triangles are congruent by AAS, ASA or HL. Domain: Cluster: Make geometric constructions Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle Domain: Enduring Understanding(s) Lesson 4.6 Isosceles and Equilateral Triangles, Vocabulary Cluster: Prove geometric theorems pp. 283-291 Many relationships exist between the measure Pythagorean triple of the angles of a triangle and the measure of Prove theorems about triangles. the sides of the triangle. Choose from the following resources to Writing in Math ensure that the intended outcome and level Domain: p. 290 #45 Challenge – proof (H.O.T. of rigor (mainly conceptual understanding Cluster: Make geometric constructions Essential Question(s) problem) and application) of the standards are met. What are the special relationships among Make formal geometric constructions angles and sides in isosceles and equilateral with a variety of tools and methods triangles? (compass and straightedge, string, Use the following Engageny Lessons to reflective devices, paper folding, introduce the concepts/build conceptual dynamic geometric software, etc.). Objective(s): understanding. If used, these lessons should be used before the lessons from the textbooks. Students will use properties of isosceles Domain: triangles. Additional Lesson(s): Cluster: Prove theorems involving similarity Students will use properties of equilateral Engageny Geometry Module 1, Topic D, Use congruence and similarity criteria triangles. Lesson 23 – Isosceles Triangles for triangles to solve problems and to Students will prove base angles of prove relationships in geometric isosceles triangles are congruent. figures. Special Segments in Triangles (Allow 2.5 weeks for instruction, review, and assessment) Domain: Enduring Understanding(s) Lesson 5.1 Bisectors of Triangles pp. 321-331 Vocabulary Cluster: Prove geometric theorems The properties of triangles create a basis for Perpendicular bisector, concurrent lines, understanding and reasoning that extends to point of concurrency, circumcenter, Prove theorems about triangles. Choose from the following resources to
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,
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