Question

What is the missing reason in the proof? Given: ∠ABC is a right angle, ∠DBC is a straight angle Prove: ∠ABC ≅ ∠ABD definition of angle bisector segment addition property definition of congruent angles transitive property

Answer 1

Answer: Definition of Angle Bisector Segment

The angle bisector theorem states that a segment bisects a triangle and equates the lengths of the other two sides of the triangle. When used to prove that ABC is congruent to ABD, the angle bisector is the segment AB. Since angle DBC is a straight angle or equal to 180 degrees, when bisected by segment AB, it forms angle ABD that is equal to 90 degrees or the exact half of 180 degrees. This therefore makes angle ABD congruent to angle ABC.

Step-by-step explanation:

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Answer 2

Answer: Definition of Angle Bisector Segment

The angle bisector theorem states that a segment bisects a triangle and equates the lengths of the other two sides of the triangle. When used to prove that ABC is congruent to ABD, the angle bisector is the segment AB. Since angle DBC is a straight angle or equal to 180 degrees, when bisected by segment AB, it forms angle ABD that is equal to 90 degrees or the exact half of 180 degrees. This therefore makes angle ABD congruent to angle ABC.