Question

a student was given the following diagram and asked to prove that angle 1 ≈ angle 2. what would be the reason for the second step in the proof? given: line A and line B are parallel. prove: angle 1 ≈ angle 2​

Answer 1

Answer: I chose b

Explanation:

Answer 2

Answer: The correct option is

(B) Corresponding angles are congruent.

Step-by-step explanation: Given that a student was told to consider the diagram and asked to prove that angle 1 ≅ angle 2.

We are to find the reason for the second step in the following proof :

(1) Line A and B are parallel Given

(2) ∠1 ≅ ∠3 ?

(3) ∠2 ≅ ∠3 ?

(4) ∠1 ≅ ∠2 ?

Since lines A and B are parallel and cut by a transversal, so angles 1 and 3 are corresponding angles. That is, ∠1. ≅ ∠3

Also, angles 2 and 3 are vertically opposite angles, so ∠2 ≅ ∠3.

And, therefore we get

∠1 ≅ ∠2.

Thus, the reason in the second step will be

angles 1 and 3 are corresponding angles and corresponding angles are congruent.

Option (B) is CORRECT.