Isosceles and Equilateral Isosceles and Equilateral TrianglesTriangles

Chapter 4 Section 5Chapter 4 Section 5

TodayToday’’s Objectives Objective

Students will use and apply properties of Students will use and apply properties of isosceles and equilateral triangles.isosceles and equilateral triangles.

Isosceles TrianglesIsosceles Triangles

BaseBase Angle Base Angle

Leg Leg

Vertex Angle

****Label your triangle exactly like this one!

LegsLegs

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

BaseBase

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

Vertex AngleVertex Angle

Created by the intersection of both legs.Created by the intersection of both legs.

It is always opposite the baseIt is always opposite the base

Base AnglesBase Angles

Created by the intersection of the base Created by the intersection of the base and the legs.and the legs.

Vertex angles are congruent to each other.Vertex angles are congruent to each other.

Isosceles Triangle TheoremIsosceles Triangle Theorem

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

Converse of the Isosceles Triangle Converse of the Isosceles Triangle TheoremTheorem

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

Turn to page 251Turn to page 251

Look at Problem 1Look at Problem 1

Try the Try the ““Got ItGot It”” problem for this example. problem for this example.

Theorem 4-5Theorem 4-5

If a line bisects the vertex angle of a If a line bisects the vertex angle of a isosceles triangle, then the line is also the isosceles triangle, then the line is also the perpendicular bisector of the base.perpendicular bisector of the base.

Turn to page 252Turn to page 252

Look at problem 2Look at problem 2

Try the Try the ““Got ItGot It”” problem on your own. problem on your own.

Corollary to Theorem 4-3Corollary to Theorem 4-3

If the triangle is equilateral, then the If the triangle is equilateral, then the triangle is equiangular.triangle is equiangular.

All equilateral triangles are equiangular.All equilateral triangles are equiangular.

Corollary to Theorem 4-4Corollary to Theorem 4-4

If a triangle is equiangular, then the If a triangle is equiangular, then the triangle is equilateral.triangle is equilateral.

All equiangular triangles are equilateral.All equiangular triangles are equilateral.

Turn to page 253.Turn to page 253.

Look at problem 3Look at problem 3

On page 253…On page 253…

Try problems #1-5 on your own.Try problems #1-5 on your own.