Question

What is the missing reason in the proof?

Given: ∠ABC is a right angle, ∠DBC is a straight angle
Prove: ∠ABC ≅ ∠ABD

A horizontal line has points D, B, C. A line extends vertically from point B to point A. Angle A B C is a right angle.



definition of angle bisector
segment addition property
definition of congruent angles
transitive property
b or d

Answer 1

The missing reason is the Angle Addition Postulate (here called the segment/angle addition property): ∠DBC = ∠ABD + ∠ABC.

Using that and the given facts (m∠DBC = 180°, m∠ABC = 90°) gives m∠ABD = 180° − 90° = 90°, so m∠ABD = m∠ABC and by the definition of congruent angles ∠ABD ≅ ∠ABC.

(So choose b: segment/angle addition property.)