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Chapter 2: Q19. (page 68)

Write a plan for a proof.

Given: ∠3is a supplement of ∠1;

∠4is a supplement of ∠2.

Prove:∠3≅∠4.

Short Answer

Expert verified

Therefore, using∠1and∠3 and∠2 and ∠4 are supplementary. It is proved that ∠3≅∠4 .

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.

Consider the following:

∠1 and∠3 and∠2 and∠4 are supplementary.

To prove ∠3≅∠4.

Since,∠1 and∠3 and∠2 and∠4 are supplementary.

Therefore,

∠1+∠3=180∘

∠2+∠4=180∘

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

Therefore,

∠1+∠3=180∘

∠1+∠4=180∘

Therefore, ∠3≅∠4(Hence proved)

03

Step 3. State the conclusion.

Therefore, using ∠1 and ∠3 and ∠2 and ∠4 are supplementary. It is proved that ∠3≅∠4.

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