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 right angle

B: substitution property

C: definition of congruent angles

Explanation:

Answer 2

Explanation:

A right angle is an angle whose measure is equal to
`90^(o)`. As the measure of two right angles equals angle on a straight line, while four right angles equal the sum of angles at a point.

Given: <ABC, <DEF are right angles.

The missing reasons in the steps of the proof are:

A: m<ABC =
`90^(o)` and m<DEF =
`90^(o)` (Meaning of a right angle)

B: m<ABC = m<DEF (By right angle property)

C: <ABC ≅ <DEF (Congruence property of angles)