Question

Copy what is shown for Theorem 3-3 on page 79. Then write a proof in two-column form.

Short answer

Proof in two column form is

Statement	Reason
1.$k\parallel n$	Given
2.$\angle 2\cong \angle 1\Rightarrow m\angle 2=m\angle 1$	Alternate interior angle
3.$m\angle 2+m\angle 4=180$	Linear pair
4.$m\angle 1+m\angle 4=180$	Substitution Property

Step-by-step solution

Step 1. Copy what is shown for Theorem 3-3 on page 79

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

Step 2. Observe from figure

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

$\angle 1$and $\angle 2$forms a pair of alternate interior angles

$\angle 4$and $\angle 2$ forms a linear pair

Step 3. Write two column proof

The proof in two column form is

Statement	Reason
1.$k\parallel n$	Given
2.$\angle 2\cong \angle 1\Rightarrow m\angle 2=m\angle 1$	Alternate interior angle
3.$m\angle 2+m\angle 4=180$	Linear pair
4.$m\angle 1+m\angle 4=180$	Substitution Property

Hence $\angle 1$is supplementary to $\angle 4$ proved