Advanced Geometry Section 3 7 The Isosceles Triangle

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Advanced Geometry Section 3. 7 The Isosceles Triangle Theorem/Converse/Inverse/Contrapositive Learner Objective: Students will solve

Advanced Geometry Section 3. 7 The Isosceles Triangle Theorem/Converse/Inverse/Contrapositive Learner Objective: Students will solve proofs and problems using heorems relating the angle measures and side lengths of triangles.

Opener: STATEMENTS REASONS Given: is a median of 1. Given 2. Given Prove: 2.

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

Theorem: If two sides of a triangle are congruent, then the angles opposite the

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

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

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

A Theorem (Inverse): If two sides of a triangle are NOT congruent, then the

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

A Theorem (Contrapositive): If two angles of a triangle are NOT congruent, then the

A 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 ). B C Given: Conclude:

Two Ways to Prove a Triangle is Isosceles: 1. Two sides are congruent ⇒

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

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

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

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