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.

A 2-column table has 8 rows. The first column is labeled Statements with entries angle A B C is a right angle, angle D B C is a straight angle, m angle A B C = 90 degrees, m angle D B C = 180 degrees, m angle A B D + m angle A B C = m angle D B C, m angle A B D + 90 degrees = 180 degrees, m angle A B D = 90 degrees, angle A B C is-congruent-to angle A B D. The second column is labeled Reasons with entries, given, given, definition of right angle, definition of straight angle, angle addition property, substitution property, subtraction property, and question mark.

definition of angle bisector
segment addition property
definition of congruent angles
transitive property

Answer 1

Step-by-step explanation:

C is a straight angle, m angle A B C = 90 degrees, m angle D B C = 180 degrees, m angle A B D + m angle A B C = m angle D B C, m angle A B D + 90 degrees = 180 degrees, m angle A B D = 90 degrees, angle A B C is-congruent-to angle A B D. The second column is labeled Reasons with entries, given, given, definition of right angle, definition of straight angle, angle addition property, substitution property, subtraction property, and question mark.

definition of angle bisector