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Chapter 2: Q23. (page 53)

Copy everything shown. Complete the proof.

Given:∠2≅∠3

Prove: ∠1≅∠4

Proof:

Short Answer

Expert verified

statements

Reasons

1.∠1≅∠2

1. vertical angles

2.∠2≅∠3

2. Given

3.∠3≅∠4

3. vertical angles

4.∠1≅∠4

4. Transitive property (used twice)

Step by step solution

01

Step 1. Write the relation between the angles ∠1 and ∠2.

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

02

Step 2. Write the relation between the angles ∠2 and ∠3.

The angles∠2 and∠3 are congruent angles as it is given that ∠2≅∠3.

03

Step 3. Write the relation between the angles ∠3 and ∠4.

From the given diagram it can be noticed that the angles∠3 and∠4 are vertical angles, therefore the angles∠3 and∠4 are congruent angles.

04

Step 4. write the relation between the angles ∠1 and ∠4.

The angles∠1 and∠4 are congruent angles by using the transitive property twice.

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