1. Lesson 4.6
Isosceles Triangles

2. 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
Base 2 1 Ð
1 and
2 are base angles
3 is the vertex angle

3. Isosceles Triangle Theorems
If two sides of a triangle are congruent, then the angles opposite those sides are congruent. A B C
Example:
Find the value of x.
By the Isosceles Triangle Theorem,
the third angle must also be x.
Therefore, x + x + 50 = 180
2x + 50 = 180
2x = 130
x = 65 x 50

4. Isosceles Triangle Theorems
If two angles of a triangle are congruent, then the sides opposite those angles are congruent. A B C
Example:
Find the value of x.
Since two angles are congruent, the
sides opposite these angles must be
congruent.
3x – 7 = x + 15
2x = 22
X = 11 50
3x - 7
x+15 A B C