Question

When writing a geometric proof, which angle relationship could be used alone to justify that two angles are congruent? 1) supplementary angles 2) linear pair of angles 3) adjacent angles 4) vertical angles

Answer 1

Recall that:

1) Two angles are supplementary angles if their measures add up to 180 degrees.

2) Linear pair of angles are two angles that form a straight angle, therefore their measures add up to 180 degrees.

3) Adjacent angles are two angles that have a common side and a common vertex (corner point) but do not overlap in any way.

4) Vertical angles are a pair of opposite angles formed by intersecting lines. Two vertical angles are always congruent.

Therefore, the only condition that guarantees the congruence of two angles is option 4.

Answer: Option 4.