Question

Given: ∠ABC is a right angle and ∠DEF is a right angle.

Prove: All right angles are congruent by showing that ∠ABC ≅∠DEF.

What are the missing reasons in the steps of the proof?

A flow chart with 4 boxes that are labeled Given, A, B, C from left to right. Box Given contains angle A B C, angle D E F are right angles. Box A contains m angle A B C = 90 degrees and m angle D E F = 90 degrees. Box B contains m angle A B C = m angle D E F. Box C contains angle A B C is-congruent-to angle D E F.



A:

B:

C:

Answer 1

A: Definition of a right angle (each right angle has measure 90°).

B: Transitive property (or substitution) of equality: since m∠ABC = 90° and m∠DEF = 90°, m∠ABC = m∠DEF.

C: Definition of congruent angles (angles with equal measures are congruent).