Transcript Isosceles and Equilateral Triangles

Isosceles and Equilateral
Triangles
Chapter 4 Section 5
Today’s Objective
 Students will use and apply properties of
isosceles and equilateral triangles.
Isosceles Triangles
Vertex Angle
Leg
Base Angle
Leg
Base
****Label your triangle exactly like this one!
Base Angle
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.