Isosceles and

Equilateral Triangles

Parts of an Isosceles Triangle

An isosceles triangle is a triangle with two congruent sides.

The congruent sides are called legs and the third side is called the base.

3

Leg Leg

Base

21

Ð1 and Ð2 are base anglesÐ3 is the vertex angle

Isosceles Triangle Theorems

Example:

x°

50°

Find the value of x.

A

B C

, .If AB AC then B C

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

Isosceles Triangle Theorems

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

Example:Find the value of x.

A

B C

50° 50°

3x - 7x+15

A

B C

, .If B C then AB AC

Equilateral Triangles

Equilateral:

A triangle in which all 3 sides are equal.

G

H I

GH = 3.7 cm

GI = 3.70cm

HI = 3.7 cm

Equilateral Triangle Theorems

• If a triangle is equilateral, then it is equiangular.

T

S R

15 in.

• If a triangle is equiangular, then it is equilateral.

What is the length of each side and angle?