Question

guided practice
proving angles congruent
congruent complements theorem
given: ∠1 and ∠2 are complementary.
∠3 and ∠2 are complementary.
prove: ∠1 ≅ ∠3
you will complete a paragraph proof of this theorem by answering a series of questions.
click or tap proof at any time to view your progress on the proof.
what definition can you use to state that m∠1 + m∠2 = 90°?
a. complementary angles
b. vertical angles
c. supplementary angles

Explanation:

To state that \( m\angle1 + m\angle2 = 90^\circ \) given \( \angle1 \) and \( \angle2 \) are complementary, we use the definition of complementary angles. By definition, complementary angles are two angles whose measures add up to \( 90^\circ \). Vertical angles are equal in measure but relate to angles formed by intersecting lines, and supplementary angles add up to \( 180^\circ \), so neither B nor C apply. Thus, the correct definition is that of complementary angles.

Answer:

A. complementary angles