Question

question 42 of 49
what is the missing reason for the 3rd step in the proof below?
given: ab || cd
prove: ∠3 ≅ ∠6
statement | reason

1. ab||cd | 1. given
2. ∠3 ≅ ∠7 | 2. corresponding angles theorem
3. ∠7 ≅ ∠6 | 3.
4. m∠3 = m∠7

m∠7 = m∠6 | 4. definition of congruence

1. m∠3 = m∠6 | 5. substitution
2. ∠3 ≅ ∠6 | 6. definition of congruence

a. if two lines are parallel, then alternate exterior angles are congruent.
b. vertical angles are congruent.
c. corresponding angles theorem.
d. if two lines are parallel, then alternate interior angles are congruent.

Explanation:

In the proof, $\angle7$ and $\angle6$ are vertical - angles. Vertical angles are always congruent. This is the reason for $\angle7\cong\angle6$.

Answer:

B. Vertical angles are congruent.