Exercise 21 Page 305

Look for vertical angles.

Statements	Reasons
1. ∠ 1 ≅ ∠ 4	1. Given
2. m∠ 1 ≅ m∠ 4	2. Definition of Congruent Angles
3. ∠ 1 ≅ ∠ 2 and ∠ 3 ≅ ∠ 4	3. Vertical Angles Theorem
4. m∠ 1 ≅ m∠ 2 and m∠ 3 ≅ m∠ 4	4. Definition of Congruent Angles
5. m∠ 2 = m∠ 3	5. Substitution Method
6. ∠ 2 ≅ ∠ 3	6. Definition of Congruent Angles

Practice makes perfect

Let's begin by graphing the lines shown in the given picture.

We are told that ∠ 1 ≅ ∠ 4, and we need to prove that ∠ 3 ≅ ∠ 4. Before making the proof, notice that both ∠ 1 and ∠ 2 as well as ∠ 3 and ∠ 4 are vertical angles. With this, we are ready to make a two-column proof table.

Statements	Reasons
1. ∠ 1 ≅ ∠ 4	1. Given
2. m∠ 1 ≅ m∠ 4	2. Definition of Congruent Angles
3. ∠ 1 ≅ ∠ 2 and ∠ 3 ≅ ∠ 4	3. Vertical Angles Theorem
4. m∠ 1 ≅ m∠ 2 and m∠ 3 ≅ m∠ 4	4. Definition of Congruent Angles
5. m∠ 2 = m∠ 3	5. Substitution Method
6. ∠ 2 ≅ ∠ 3	6. Definition of Congruent Angles

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