Question

Janet is trying to prove that the sum of the measures of the interior angles of a triangle is 180°.

Which reason can she use to justify the statement in line 6?
A
Alternate interior angles of parallel lines are congruent

B
Corresponding angles of parallel lines are congruent

C
Exterior Angle Theorem

D
Symmetric Property

Answer 1

A . Alternate interior angles of parallel lines are congruent

Explanation:

If you observe the image, the statement that Janet wants to justify is

`\angle 1 \cong \angle A`

`\angle 3 \cong \angle C`

According to the given graph, these angles are inside parallels because
`DE \parallel AC` by given, and these angles are at different sides of the transversals
`BA` and
`BC`, those position define Alternate Interior Angles, which by theorem they are congruent.

Therefore, the right reason of such congruence is

A . Alternate interior angles of parallel lines are congruent.

Answer 2

A Alternate interior angles of parallel lines are congruent

Explanation:

The referenced angles (1, A), (3, C) are alternate interior angles, not corresponding or exterior. The symmetric property does not apply. The only answer choice with any applicability is the one shown above. (It is also the right choice.)