1. Advanced Geometry
Section The Isosceles Triangle Theorem/Converse/Inverse/Contrapositive
Learner Objective: Students will solve proofs and problems using
 theorems relating the angle measures and side lengths of triangles.

2. Opener: Given: is a median of Prove: 1. 1. Given 2. med. of 2. Given
STATEMENTS
REASONS 1. 1.
Given 2.
med. of 2.
Given 3. 3.
Median divides a side
of a into 
segments. (Def. Med.) 4. 4.
Reflexive Prop. 5. 5.
SSS Post. (1, 3, 4) 6. 6.
CPCTC

3. If two sides of a triangle are congruent,
Theorem:
If two sides of a triangle are congruent,
then the angles opposite the sides are congruent. 
(If , then ).
Given:
Conclude:

4. If two angles of a triangle are congruent,
Theorem (Converse):
If two angles of a triangle are congruent,
then the sides opposite the angles are congruent. 
(If , then ).
Given:
Conclude:

5. If two sides of a triangle are NOT congruent, B C
Theorem (Inverse):
If two sides of a triangle are NOT congruent,
then the angles opposite the sides are NOT 
congruent and the larger angle is opposite the
longer side (If , then ).
Given:
Conclude:

6. Theorem (Contrapositive): B C
Theorem (Contrapositive):
If two angles of a triangle are NOT congruent,
then the sides opposite the angles are NOT congruent 
and the longer side is opposite the
larger angle (If , then ).
Given:
Conclude:

11. 1. Two sides are congruent ⇒ isosceles.
Two Ways to Prove a Triangle is Isosceles:
1. Two sides are congruent ⇒ isosceles.
2. Two angles are congruent ⇒ isosceles.

21. HW:
Pg. 152
#1-4,10,11,15