Question

What is the missing piece of the information in the paragraph proof?

Answer 1

Answer:

The correct option is a.

Step-by-step explanation:

Given: ∠1 and ∠2 are supplementary angles.

Prove: l║m

Proof:

It is given that ∠1 and ∠2 are supplementary angles.

$\angle 1+\angle 2=180^{\circ}$           .... (1)

∠1 and ∠3 are supplementary angles because both angles lie on a straight line.

$\angle 1+\angle 3=180^{\circ}$           .... (2)

Using (1) and (2), we get

$\angle 1+\angle 2=\angle 1+\angle 3$

Subtract angle 1 from both the sides.

$\angle 2=\angle 3$

$\angle 2\cong \angle 3$

Since ∠2 ≅ ∠3 are corresponding angles,

$l\parallel m$

Hence proved.

Therefore the missing statement is $\angle 2=\angle 3$ and option a is correct.

Answer 2

B. angle 2 and angle 3 and congruent.

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