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Name: ____________________________________________ Date: ______________ Honors Geometry Section 2.4 Notes: Congruent Supplements and Complements Theorem 4: If angles are supplementary to the same angle, then they are congruent. Proof: Given: ∠1 is supplementary to ∠2 ∠3 is supplementary to ∠2 Prove: ∠1 ≅ ∠3 Statement Reason 1. 1. 2. 2. 3. 3. 4. 4. 5. 5. 6. 6. 7. 7. 8. 8. Theorem 5: If angles are supplementary to congruent angles, then they are congruent. Theorem 6: If angles are complementary to the same angle, then they are congruent Theorem 7: If angles are complementary to congruent angles, then they are congruent. Proofs for these theorems are very similar to the proof for Theorem 4. We will not do them all in class. Example 1 Given: ∠1 is supplementary to ∠2 ∠3 is supplementary to ∠4 ∠1 ≅ ∠4 Prove: ∠2 ≅ ∠3 Statement Reason Example 2 Given: ∠ is complementary to ∠ ∠ is complementary to ∠ Prove: ∠ ≅ ∠ Statement Reason Example 3: Given: Diagram as Shown Prove: ∠ ≅∠ Statement Reason Example 4: Given: ∠ ≅∠ Prove: ∠ ≅∠ Statement Reason