Question

problem 11: (first taught in lesson 23)
from this given statement, select the definition, property, postulate, or theorem that justifies the prove statement.
given: $overline{ut}paralleloverline{ws}$
prove: $angle1congangle5$
a
b
c
d
e
if two parallel lines are cut by a transversal, then their alternate exterior angles are congruent.

Explanation:

Step1: Identify parallel lines

Given $\overline{UT}\parallel\overline{WS}$.

Step2: Identify angles

$\angle1$ and $\angle5$ are alternate - exterior angles formed by the transversal intersecting $\overline{UT}$ and $\overline{WS}$.

Step3: Apply theorem

By the alternate - exterior angles theorem, if two parallel lines are cut by a transversal, alternate exterior angles are congruent. So $\angle1\cong\angle5$.

Answer:

A. If two parallel lines are cut by a transversal, then their alternate exterior angles are congruent.