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

Answer:

(C) Alternate interior angles are congruent.

Step-by-step 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.