When writing a geometric proof, which angle relationship could be used alone to justify that two angles are congruent?
2 answers:
Answer:
Vertical angles are always congruent.
Step-by-step 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
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