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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 : 34.

Short Answer

Expert verified

The proof in two column form is:

1+3=180°

Supplementary angles.

2+4=180°

Supplementary angles.

1=2

Vertically opposite angles.

1+4=180°

1=2

3=4

1+4=1+3

Step by step solution

01

Step 1. Observe the diagram.

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

The diagram is:

02

Step 2. Show the proof.

∠1 and∠3 are supplementary.

So, 1+3=180°

∠2 and∠4 are supplementary.

So,2+4=180°

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

So, 1=2.

Then, 1+4=180°as 1=2.

Therefore,

3=4since 1+4=1+3.

03

Step 3. State the conclusion.

The proof in two column form is:

1+3=180°

Supplementary angles.

2+4=180°

Supplementary angles.

1=2

Vertically opposite angles.

1+4=180°

1=2

3=4

1+4=1+3

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