1. (The Isosceles Triangle Theorems)
Chapter 4 Section 4
(The Isosceles Triangle Theorems)
Isosceles Triangle
a triangle with at least two congruent sides

2. Vertex Angle
Leg
Leg
Base Angle
Base
Base Angle

3. Given:
Prove: A 1 2 C B D

4. A B 1 D B C A C D 2 A
Statements
Reasons

5. A B 1 D C D 2 A
Statements
Reasons
Given

6. A B 1 D C D 2 A
Statements
Reasons
Def. angle bisector

7. A B 1 D C D 2 A
Statements
Reasons
Reflexive Property

8. A B 1 D C D 2 A
Statements
Reasons

9. Statements Reasons A B 1 D B C A C D 2 AA B 1 D B C A C D 2 A
Statements
Reasons
Corresponding parts of congruent triangles are congruent.

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

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

12. Corollary
An equilateral triangle is also equiangular.
(An equiangular triangle is also equilateral.)

13. Corollary
The bisector of the vertex angle of an isosceles triangle
is perpendicular to its base
at its midpoint.

14. Solve for x. (Assume that the measurements for the diagram on the left are given in degrees.)

15. Solve for x.

16. M R T S P Q
Statements
Reasons

17. M R T S P Q
Statements
Reasons

18. Homework Chapter 4 Section 4 (The Isosceles Triangle Theorems)
Chapter 4 Section 4
(The Isosceles Triangle Theorems)
Homework
Section 4.4 Classroom Exercises (p. 136) #1-7
Section 4.4 Written Exercises (p. 137) #1-9
Chapter 4 Mid-Review Worksheet