Question

Write proof in two column form

Given: $k\parallel l$

Prove: $\angle 2\cong \angle 7$

Short answer

Proof in two column form is

Statement	Reason
1. $k\parallel l$	Given
2. $\angle 2\cong \angle 5$	Vertically opposite angle
3. $\angle 5\cong \angle 7$	Corresponding angle
4. $\angle 2\cong \angle 7$	Transitive 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

$\angle 2$and $\angle 5$are vertically opposite angles, so they are congruent

$\angle 2\cong \angle 5$

Step 3. Corresponding angles

$\angle 5$and $\angle 7$forms a pair of corresponding angles which are congruent$\angle 5\cong \angle 7$

Step 4. Use transitive property

If $a=b$and $b=c$then$a=c$

Since, $\angle 2\cong \angle 5$and $\angle 5\cong \angle 7$implies$\angle 2\cong \angle 7$

Thus, proof in two column form is

Statement	Reason
1. $k\parallel l$	Given
2. $\angle 2\cong \angle 5$	Vertically opposite angle
3. $\angle 5\cong \angle 7$	Corresponding angle
4. $\angle 2\cong \angle 7$	Transitive Property