1. Warm up… Supply the reasons in the two column proof and turn it in
Given: A is the midpoint of MT, A is the midpoint of SR.
Prove: MS ║TR.
Statements:
1. A is the midpoint of MT, A is the midpoint of SR.
2. MA ≅ TA, SA ≅ RA
3. MAS ≅ TAR
4. ∆MAS ≅ ∆TAR
5. M ≅ T
6. MS ║ TR

2. 4-5 isosceles and equilateral triangle

3. Isosceles triangles
legs
base
Base angles

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

5. Example 1
In isosceles triangle ISO with base SO. If and , find the measure of each angle of the triangle.

6. Converse of Isosceles triangle theorem
If two angles of a triangle are congruent, then the sides opposite the angles are congruent.

7. theorem
The bisector of the vertex angles of an isosceles triangle is the perpendicular bisector of the base.

8. Corollary
A triangles is equilateral if and only if it is equiangular.

9. Example 2
The measure of the vertex angle of an isosceles triangle is 20. Find the measure of each base.

10. Example 3
In triangle PQR, angles P and Q are congruent. Segment PR is 16 and the perimeter is 36. Find QP.

11. Example 5
Given:
Prove: 1 R 4 T 3 Q 2