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3.7 Angle Side Theorems Theorem 20: Isosceles Triangle Theorem (ITT) If 2 sides of a triangle are congruent, then the angles opposite the sides are congruent. A A If then B C B C Theorem 21: Converse Isosceles Triangle Theorem (CITT) If 2 angles of a triangle are congruent, then the sides opposite the angles are congruent. A A If then B C B C 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. Given: D E H EF HG Prove: DF DG Statements 1. E H Reasons 1. Given EF HG 2. DE DH 3. DEF DHG 4. DF DG 2. CITT If 3. SAS 4. CPCTC E then F G H Given: XY XZ Prove: 1 2 X 1 Y Statements 1. XY XZ 2 Z Reasons 1. Given 2. XYZ XZY 2. If 2. ITT 3. 1 is suppl. to XYZ 3. If 2 angles form a straight line, then 2 is suppl. to XZY 4. 1 2 then they are supplementary 4. If 2 angles are supplementary to 4. ST congruent angles then they are congruent More Practice Proofs More Practice Proofs