Advanced Geometry Section 3.7 The Isosceles Triangle Theorem/Converse/Inverse/Contrapositive Learner Objective: Students will solve proofs and problems.

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Presentation transcript:

Advanced Geometry Section 3.7 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.

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 2  segments. (Def. Med.) 4. 4. Reflexive Prop. 5. 5. SSS Post. (1, 3, 4) 6. 6. CPCTC

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:

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:

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:

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:

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.

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