Question

which of the following statements justify why vertical angles are congruent? select all that apply. a) vertical angles are complementary to the same angle. b) vertical angles are supplementary to the same angle. c) vertical angles are the same angle. d) given a pair of vertical angles, rotating one angle 180° about its vertex will map the angle onto the other angle in the pair. e) given a pair of vertical angles, reflecting one angle over one of its sides will map the angle onto the other angle in the pair. f) given a pair of vertical angles, translating one angle along one of its sides will map the angle onto the other angle in the pair.

Explanation:

Vertical angles are congruent because they are supplementary to the same angle. Also, rotating one vertical - angle 180° about its vertex maps it onto the other angle in the pair. Complementary angles add up to 90°, and vertical angles are not complementary to the same angle. Vertical angles are not the same angle. Reflection or translation of one vertical angle will not map it onto the other.

Answer:

B. Vertical angles are supplementary to the same angle.
D. Given a pair of vertical angles, rotating one angle 180° about its vertex will map the angle onto the other angle in the pair.