Mod 15.2: Isosceles and Equilateral Triangles

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Presentation transcript:

Mod 15.2: Isosceles and Equilateral Triangles Essential Question: What are the special relationships among angles and sides in isosceles and equilateral triangles? CASS: G-CO.10 Prove theorems about triangles. MP.3 Logic

Anatomy of Isosceles Triangles EXPLORE 1 Anatomy of Isosceles Triangles Isosceles triangle = A a triangle with at least two congruent sides. vertex angle leg leg base angles B C base Given is isosceles, what can we state about

Isosceles Triangle Theorem (aka Base Angles Theorem) EXPLAIN 1 p. 740 Isosceles Triangle Theorem (aka Base Angles Theorem) B If two sides of a triangle are congruent, then the angles opposite them are congruent. A C If , then .

Converse of the Isosceles Triangle Theorem EXPLAIN 1 p. 740 Converse of the Isosceles Triangle Theorem (aka Base Angles Converse Theorem) A B C If two angles of a triangle are congruent, then the sides opposite them are congruent. If , then .

EXAMPLE 3 p. 744 3x + 3 + 3x + 3 + 5x – 2 = 180 11x + 4 = 180 m∠P = (3x - 3)° = [3(16) – 3]° = (48 – 3)° = 45° So the length of each side of the triangle is 15 cm.