Question

Write proofs in two-column form.

Given: $k\parallel l$

Prove: $\angle 1$is supplementary to $\angle 7$

Short answer

Proof in two column form is

Statement	Reason
1.$k\parallel l$	Given
2.$\angle 4\cong \angle 7$	Vertically opposite angle
3.$m\angle 1+m\angle 4=180$	Same side interior angle
4.$m\angle 1+m\angle 7=180$	Substitution Property

Step-by-step solution

Step 1. Observations from figure

Line $t$is transversal to the parallel lines $k$and$I$

Step 2. Vertically opposite angle

$\angle 4$and $\angle 7$are vertically opposite angles, so they are congruent

$\begin{array}{c}\angle 4\cong \angle 7\\ m\angle 4=m\angle 7\end{array}$

Step 3. Same-side interior angles

$\angle 1$and $\angle 4$forms a pair of same-side interior angles

Theorem 3-3: If two parallel lines are cut by a transversal then the same-side interior angles are supplementary.

$m\angle 1+m\angle 4=180$ (1)

Step 4. Use substitution property

Substitute $m\angle 7$for $m\angle 4$in equation (1)

$m\angle 1+m\angle 7=180$

Thus, proof in two column form is

Statement	Reason
1.$k\parallel l$	Given
2.$\angle 4\cong \angle 7$	Vertically opposite angle
3.$m\angle 1+m\angle 4=180$	Same side interior angle
4. $m\angle 1+m\angle 7=180$	Substitution Property