Isosceles and Equilateral Triangles Skill 22 Objective HSGCO

Isosceles and Equilateral Triangles Skill 22

Objective HSG-CO. 10: Students are responsible for using and applying properties of isosceles and equilateral triangles.

Remember… Isosceles Triangles Equilateral Triangles - 2 sides are congruent - 3 sides are congruent - 2 base angles are congruent - 3 angles are congruent

Theorem 20; Isosceles Triangle Theorem If two sides of a triangle are congruent, then the angles opposite those sides are congruent. X Y B Z

Theorem 20; Isosceles Triangle Theorem Statement Reason 1) Given 2) Def. ∠ Bisector X Y B 3) Reflexive Prop. 4) SAS Postulate 5) C. P. C. T. Z

Theorem 21; Converse of Iso. ∆ Theorem If two angles of a triangle are congruent, then the sides opposite those angles are congruent. X Y Z

Theorem 22; Angle Bisector of Iso. ∆ Thm. If a line bisects the vertex angles of an isosceles triangle, then the line is also the perpendicular bisector. X Y B Z

Corollary to Thm. 20: Equilateral → Equiangular If a triangle is equilateral, then the triangle is equiangular. X Y Z

Corollary to Thm. 21: Equiangular → Equilateral If a triangle is equiangular, then the triangle is equilateral. X Y Z

Example 1: Using Isosceles Triangle Theorems B D A E C

Example 1: Using Isosceles Triangle Theorems B D A E C

Example 2: Using Algebra B What is the value of x? Explain. A xᵒ 54ᵒ D C

Example 3: Finding Angle Mearues What are the measures of ∠A, ∠B, and ∠ADC? Explain. All triangles are equilateral. So, they are equiangular too. A D C B

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