3. 4.4 The Isosceles Triangle Theorems
Objectives:
Legs/base
Isosceles Triangle Th.

4. What is an isosceles triangle?
Is an equilateral triangle also isosceles? How often?
So does that mean that everything we learn about isosceles triangles is also true for equilateral triangles?

6. The Isosceles Triangle Theorem
Some additional information that will allow us to prove more triangles congruent
The Isosceles Triangle Theorem
If 2 sides of a triangle are congruent, then the angles opposite those sides are congruent. A B C

8. This can be proven by the following proof.
Given :
Prove: B C

9. Corollaries that follow
An equilateral triangle is also equiangular
An equilateral triangle has three 60° angles
The bisector of the vertex angle of an isosceles triangle is perpendicular to the base at its midpoint (the bisector of the vertex angle is the perpendicular bisector of the base)

10. Given: Triangle ABC is an isosceles triangle with base BC.
Prove: AX is perpendicular bisector of BC. A B C

11. Converse of the Isosceles Triangle Theorem
If 2 angles of a triangle are congruent, then the sides opposite those angles are congruent. A B C

19. B E D A C 1 4 2 3
Lets use the common segment theorem, redraw the pic with these triangles separated.

20. Find each indicated measureX
70° Y Z

21. B
65° A D C

23. M N X L

24. A B C