Question

12. Complete the two-column proof.
(6 points)
Given: 22 and 25 are supplementary
Prove: ? || m

Answer 1

When a transversal cuts through a pair of parallel lines, it creates pairs of angles with special properties.

The complete proof is:

• $\mathbf{\angle 2\ and\ \angle 5}$ are supplementary angles --- Given.
• $\mathbf{\angle 3 \cong \angle 2}$ --- vertical angle theorem.
• $\mathbf{\angle 2\ and\ \angle 5}$ are supplementary angles --- Same side interior angle.
• $\mathbf{l \ ||\ m}$ -- Proved.

From the question, we have the following given parameter

$\mathbf{\angle 2\ and\ \angle 5}$ are supplementary angles

So, the first blanks are:

• $\mathbf{\angle 2\ and\ \angle 5}$ are supplementary angles --- Given.

Next, we have:

$\mathbf{\angle 3 \cong \angle 2}$

This is because both angles are vertical angles

So, the second blank is: vertical angle theorem.

Also,

Angles 3 and 5 are supplementary angles because they add up to 180 degrees, and they are both at the same interior side of the transversal.

So, the third blank is Same side interior angle.

The above highlights mean that $\mathbf{l \ ||\ m}$ has been proved.

So, the last blanks are:

• $\mathbf{l \ ||\ m}$ -- Proved

Read more about two-column proofs at:

https://brainly.com/question/9198561