1. 3.7 Angle Side Theorems

2. Theorem 20: Isosceles Triangle Theorem (ITT) If 2 sides of a triangle are congruent, then the angles opposite the sides are congruent. A BC A BC Ifthen

3. Theorem 21: Converse Isosceles Triangle Theorem (CITT) If 2 angles of a triangle are congruent, then the sides opposite the angles are congruent. A BC A BC Ifthen

4. Can you prove theorems 20 &21? ITT can be proven using SSS by naming the triangle in a correspondence with itself. CITT can be proven using ASA by naming the triangle in a correspondence with itself. Special Note: for triangles, equilateral and equiangular will be used interchangeably.

5. Given: Prove: E F G H D Statements Reasons 1. 1. Given 2. 2. If then 3. SAS 4. CPCTC 3. 4. 2. CITT

6. Given: Prove: X Z Y 1 2 Statements Reasons 1. Given 1. 2. If then 3.If 2 angles form a straight line, then they are supplementary 4.If 2 angles are supplementary to congruent angles then they are congruent 2. 3. 4. 2. ITT 4. ST

7. More Practice Proofs