McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
4. Proving Angle Relationships
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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