Exercise 28 Page 306

Statements	Reasons
1. ∠ 1 and ∠ 3, ∠ 2 and ∠ 4 are vertical angles	1. Given
2. m∠ 1+m∠ 2=180	2. Supplement Theorem
3. m∠ 2+m∠ 3=180	3. Supplement Theorem
4. ∠ 1≅ ∠ 3	4. Congruent Supplements Theorem
5. m∠ 2+m∠ 3=180	5. Supplement Theorem
6. m∠ 3+m∠ 4=180	6. Supplement Theorem
7. ∠ 2≅ ∠ 4	7. Congruent Supplements Theorem

Practice makes perfect

Let's begin by remembering what Theorem 2.8 states.

If two angles are vertical angles then they are congruent.

We can make a graph that illustrates this situation.

In the graph above both ∠ 1 and ∠ 3, as well as ∠ 2 and ∠ 4, are vertical angles. Our job is to prove that ∠ 1≅ ∠ 3 and ∠ 2≅ ∠ 4.

Statements	Reasons
1. ∠ 1 and ∠ 3, ∠ 2 and ∠ 4 are vertical angles	1. Given
2. m∠ 1+ m∠ 2=180	2. Supplement Theorem
3. m∠ 2+ m∠ 3=180	3. Supplement Theorem
4. ∠ 1≅ ∠ 3	4. Congruent Supplements Theorem
5. m∠ 2+ m∠ 3=180	5. Supplement Theorem
6. m∠ 3+ m∠ 4=180	6. Supplement Theorem
7. ∠ 2≅ ∠ 4	7. Congruent Supplements Theorem

Hints