Question

prove ∠1 ≅ ∠5
statements reasons
1 m || n given
2 ∠1 ≅ ∠7 alternate exterior angle theorem
3 ? vertical angles theorem
4 ∠1 ≅ ∠5 transitive property of congruence
which statement is missing in the proof?
a. ∠1 ≅ ∠6
b. ∠3 ≅ ∠7
c. m∠5 + m∠7 = 180°
d. ∠7 ≅ ∠5

Explanation:

Step1: Recall vertical - angles concept

Vertical angles are congruent. We need to find a pair of vertical angles related to ∠1 or ∠5. Since we know ∠1≅∠7 and we want to prove ∠1≅∠5, we look for an angle that is vertical to ∠5 and related to ∠7.

Step2: Identify the vertical - angle pair

∠5 and ∠7 are vertical angles. According to the vertical - angles theorem, vertical angles are congruent. So the missing statement is ∠7≅∠5.

Answer:

D. ∠7≅∠5