Question

What is the missing reason for the 3rd step in the proof below?

A. If two lines are parallel, then alternate interior angles are congruent
B. Corresponding angles theorem
C. Vertical angles are congruent
D. If two lines are parallel, then alternate exterior angles are congruent

Answer 1

The missing reason for the 3rd step in the proof below is;

C. Vertical angles are congruent

Explanation:

In the two column proof, we have;

Statement
`{}` Reason

1. AB ║ CD
`{}` 1. Given

2. ∠3 ≅ ∠7
`{}` 2. Corresponding angles theorem

3. ∠7 ≅ ∠6
`{}` 3. Vertical angles are congruent

4. m∠3 = m∠7
`{}` 4. Definition of congruence

m∠7 = m∠6

5. m∠3 = m∠6
`{}` 5. Substitution

6. m∠3 ≅ m∠6
`{}` 6. Definition of congruence

Vertical angles are the angles formed on the opposite sides of two straight lines when they cross each other

Other vertical angles in the diagram are;

1) ∠5 and ∠8

2) ∠1 and ∠4

3) ∠2 and ∠3