Exercise 15 Page 305

Let's begin by looking at the given information and what we want to prove. Given:& ∠ 5 ≅ ∠ 6 Prove:& ∠ 4 and ∠ 6 are supplementary

Let's highlight the congruent parts in the given diagram.

Notice that ∠ 4 and ∠ 5 form a linear pair. With this information, we are ready to write a two-column proof.

Statements	Reasons
1. ∠ 5 ≅ ∠ 6	1. Given
2. m ∠ 5 = m ∠ 6	2. Definition of congruent angles
3. m ∠ 4 + m ∠ 5 =180	3. Supplement Theorem
4. m ∠ 4 + m ∠ 6 =180	4. Substitution Method
5. ∠ 4 and ∠ 6 are supplementary	5. Definition of supplementary angles