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Chapter 2: Q8. (page 62)

Describe your plan for proving the following. You don’t need to give all the details.

Given:∠3 is supplementary to∠1;∠4 is supplementary to∠2.

Prove: ∠3≅∠4

Short Answer

Expert verified

∠3 and ∠4 are equivalent.

Step by step solution

01

Step 1. Observe the given diagram.

The given diagram is:

02

Step 2. Definition of supplementary angles.

The supplementary angles are the angles whose sum is 180°.

03

Step 3. Write the proof of the statement ∠3≅∠4.

∠3 is supplementary to∠1 and∠4 is supplementary to∠2.

Therefore, the sum of angles ∠3 and ∠1 is 180° and the sum of angles ∠4 and ∠2 is also 180°.

That implies,

∠3+∠1=180°1and ∠4+∠2=180°2.

Subtract equation (2) from equation (1).

∠3+∠1−∠4+∠2=180°−180°∠3+∠1−∠4−∠2=03

From the given diagram it can be noticed that angles ∠1 and ∠2 are the vertical angles.

As, angles ∠1 and ∠2 are congruent angles, therefore ∠1=∠2.

Substitute the above relation in equation (3).

∠3+∠1−∠4−∠2=0∠3+∠2−∠4−∠2=0∠3−∠4=0∠3=∠4

Therefore, ∠3≅∠4.

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