1. The Isosceles Triangle Theorems
Base Angles and Opposite Sides
Hypotenuse - Leg

2. Parts of an Isosceles Triangle

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

4. Isosceles Triangle Theorem
If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
Given:
Bisect angle A
So by SAS So
By C.P.C.T.

5. Corollary of Isosceles Triangle Theorem
An equilateral triangle is also equiangular
An equilateral triangle has three 60 degree angles.
The bisector of the vertex angle of an isosceles triangle is perpendicular to the base at its midpoint.

6. Another Theorem
If two angles of a triangle are congruent, then the sides opposite those angles are congruent.
What is this compared to
the Isosceles Triangle Theorem?
An equiangular triangle is also equilateral.

7. Solve for x and y

8. Solve for angles… 2,3,4
Given:

9. Hypotenuse – Leg (HL)
In two right triangles if the hypotenuse and one leg are congruent, then the triangles are congruent.
To use this you must show Right Triangles

10. Solve for v

11. Find the missing side