Question

proof complete the two - column proof. the statements are provided on the left. drag the reasons to the corresponding stateme
given: ( angle 5 cong angle 7 )
prove: ( angle 5 cong angle 8 )
proof:

1. ( angle 5 cong angle 7 )
2. ( angle 7 cong angle 8 )
3. ( angle 5 cong angle 8 )

Explanation:

Step1: Given

The first statement $\angle5\cong\angle7$ is given in the problem.

Step2: Vertical angles are congruent

$\angle7$ and $\angle8$ are vertical angles. By the vertical angles theorem, vertical angles are congruent. So, $\angle7\cong\angle8$.

Step3: Transitive property of congruence

If $\angle5\cong\angle7$ and $\angle7\cong\angle8$, then by the transitive property of congruence (if \(a = b\) and \(b = c\), then \(a = c\)), we have $\angle5\cong\angle8$.

Answer:

1. Given
2. Vertical angles are congruent
3. Transitive property of congruence