Question

Which reason justifies Statement 3?

A) Vertical angles are congruent.
B) Corresponding angles are congruent.
C) Alternate interior angles are congruent.
D) Alternate exterior angles are congruent.

Answer 1

c alt int angles are congruent. tattoo that one on your arm it's very important!

Answer 2

(C) Alternate interior angles are congruent.

Explanation:

Given: Lines A and B are parallel lines and C and D are transversals.

To prove:
`{\angle}X+{\angle}Y+{\angle}Z=180^(\circ)`

Proof:

Statement Reason

1. Lines A and B are parallel lines; Given

C and D are transversals

2.∠Y≅∠4 Alternate interior angles

3.∠Z≅∠6 Alternate interior angles

4.∠X+∠4+∠6=180° Straight line property

5. ∠X+∠Y+∠Z=180° Substitution property

Hence proved.

Therefore, option C is correct.