Isosceles and Equilateral Triangles Chapter 4 Section 5

Today’s Objective  Students will use and apply properties of isosceles and equilateral triangles.

Isosceles Triangles Base Base Angle Leg Vertex Angle ****Label your triangle exactly like this one!

Legs  Legs are congruent  They connect the base to the vertex angle.

Base  The third side of an isosceles triangle.  It is always opposite the vertex angle.

Vertex Angle  Created by the intersection of both legs.  It is always opposite the base

Base Angles  Created by the intersection of the base and the legs.  Vertex angles are congruent to each other.

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 a triangle are congruent, then the sides opposite those angles are congruent.

Turn to page 251  Look at Problem 1  Try the “Got It” problem for this example.

Theorem 4-5  If a line bisects the vertex angle of a isosceles triangle, then the line is also the perpendicular bisector of the base.

Turn to page 252  Look at problem 2  Try the “Got It” problem on your own.

Corollary to Theorem 4-3  If the triangle is equilateral, then the triangle is equiangular.  All equilateral triangles are equiangular.

Corollary to Theorem 4-4  If a triangle is equiangular, then the triangle is equilateral.  All equiangular triangles are equilateral.

Turn to page 253.  Look at problem 3

On page 253…  Try problems #1-5 on your own.