Isosceles and Equilateral Triangles Isosceles Triangle Vocabulary: Vertex Angle – The angle formed by the congruent sides of an isosceles triangle. Base.

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Presentation transcript:

Isosceles and Equilateral Triangles Isosceles Triangle Vocabulary: Vertex Angle – The angle formed by the congruent sides of an isosceles triangle. Base Angles – The two angles formed by the base and one of the congruent sides of an isosceles triangle.

Isosceles and Equilateral Triangles Isosceles Triangle Theorem If two sides of a triangle are congruent, then the angles opposite those sides are congruent. Converse of the Isosceles Triangle Theorem If two angles of an isosceles triangle are congruent, then the sides opposite those angles are congruent.

Example 6-1c Write a two-column proof. Given:. Prove:

Example 6-1d Proof: ReasonsStatements 1. Given 3. Isosceles  Theorem 2. Def. of isosceles triangles  ADB is isosceles Given 5. Def. of midpoint 6. SAS 7.7. CPCTC 6.  ABC  ADC

Example 6-2e Answer: A Multiple-Choice Test Item If and what is the measure of A. 25 B. 35 C. 50 D. 130

Example 6-3c a. Name two congruent angles. Answer: b. Name two congruent segments.

Isosceles and Equilateral Triangles Corollary 4.3 A triangle is equilateral if and only if it is equiangular. Corollary 4.4 Each angle of an equilateral triangle measures 60 degrees.

a. Find x. Example 6-4d b. Answer: 90 Answer: 30  ABC is an equilateral triangle. bisects