1. Lesson 3-2
Isosceles Triangles

2. Parts of An Isosceles Triangle
An isosceles triangle is a triangle with at least two congruent sides.
The congruent sides are called legs and the third side is called the base.
The angles adjacent to the base are called base angles.
The angle opposite the base is called the vertex angle.
and are legs.
is the base.
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.

4. Isosceles Triangle Theorems
If two angles of a triangle are congruent, then the sides
opposite those angles are congruent.

5. Example 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

6. More Examples Since two angles are congruent, the
sides opposite these angles must be
congruent.
3x – 7 = x + 15
2x = 22
x = 11

7. Equilateral and Equiangular Triangles
Corollary: If a triangle is equilateral, then …
it is equiangular. .

8. Equilateral and Equiangular Triangles
Corollary: If a triangle is equiangular, then…
it is equilateral. .

9. What if all the ANGLES in a triangle are DIFFERENT?
Then the triangle is SCALENE
because all of the sides are DIFFERENT too!