Question

Provide reasons for the statements.

Given: <1 and <3 are vertical angles.
Prove: <1 =~ <3

Answer 1

1. ∠1 and ∠3 are vertical angles. 1. Given

2. ∠1 and ∠2 form a linear pair.

∠2 and ∠3 form a linear pair. 2. Definition of linear pair

3. ∠1 and ∠2 are supplementary.

∠2 and ∠3 are supplementary. 3.

4. m∠1 + m∠2 = 180˚

m∠2 + m∠3 = 180˚ 4.

5. m∠1 + m∠2 = m∠2 + m∠3 5.

6. m∠1 = m∠3 6.

7. ∠1 ≅ ∠3 7. Given

Explanation: