Question

Write a proof in two-column form for Exercise 19.

Exercise 19:Write a plan for a proof.

20. Given:∠3 is a supplement of∠1;

∠4 is a supplement of∠2.

Prove : $\angle 3\cong \angle 4$.

Short answer

The proof in two column form is:

$\angle 1+\angle 3=180°$	Supplementary angles.
$\angle 2+\angle 4=180°$	Supplementary angles.
$\angle 1=\angle 2$	Vertically opposite angles.
$\angle 1+\angle 4=180°$	$\angle 1=\angle 2$
$\angle 3=\angle 4$	$\angle 1+\angle 4=\angle 1+\angle 3$

Step-by-step solution

Step 1. Observe the diagram.

∠3 is a supplement of∠1 and∠4 is a supplement of∠2.

The diagram is:

Step 2. Show the proof.

∠1 and∠3 are supplementary.

So, $\angle 1+\angle 3=180°$

∠2 and∠4 are supplementary.

So,$\angle 2+\angle 4=180°$

Also, ∠1 and ∠2 both are vertically opposite angle.

So, $\angle 1=\angle 2$.

Then, $\angle 1+\angle 4=180°$as $\angle 1=\angle 2$.

Therefore,

$\angle 3=\angle 4$since $\angle 1+\angle 4=\angle 1+\angle 3$.

Step 3. State the conclusion.

The proof in two column form is:

$\angle 1+\angle 3=180°$	Supplementary angles.
$\angle 2+\angle 4=180°$	Supplementary angles.
$\angle 1=\angle 2$	Vertically opposite angles.
$\angle 1+\angle 4=180°$	$\angle 1=\angle 2$
$\angle 3=\angle 4$	$\angle 1+\angle 4=\angle 1+\angle 3$