Question

When writing a geometric proof, which angle relationship could be used alone to justify that two angles are congruent?

Answer 1

Vertical angles i believe is the right answer to this problem

Answer 2

Vertical angles are always congruent.

Explanation:

Vertical angles are always congruent, but congruent angles do not have to be vertical. Any two angles with the same angle measurement are considered congruent by definition.

Imagine (or draw):

an X forming 2 pairs of vertical angles. ∠1 is to the left, ∠2 is on top, ∠3 is to the right, and ∠4 is on the bottom. Vertical angles are always congruent because ∠1 and ∠2 are supplementary, meaning that their measures add to 180 degrees. The measures of ∠2 and ∠3 also add to 180 degrees. This means that:

m∠1+m∠2=180 and m∠2+m∠3=180.

Using the Transitive Property, it becomes m∠1+m∠2=m∠2+m∠3.

If you subtract the measure of ∠2 from both sides,

it becomes m∠1=m∠3