Question

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

Answer 1

Answer:

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

C. Vertical angles are congruent

Step-by-step 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