Question

Given: m∠ABC = m∠CBD

Prove: Ray B C bisects ∠ABD.

3 lines extend from point B. One line extends to point A, another to C, and another to D.
Justify each step in the flowchart proof.


A flow chart with 3 boxes that are labeled A, B, C, from top to bottom. Box A contains m angle A B C = m angle C B D. Box B contains angle A B C is-congruent-to angle C B D. Box C contains Ray B C bisects angle A B D.



A:

B:

C:

Answer 1

A: Given — m∠ABC = m∠CBD.

B: ∠ABC ≅ ∠CBD — If two angles have equal measures, then the angles are congruent (definition of congruent angles).

C: Ray BC bisects ∠ABD — If a ray divides an angle into two congruent angles, then the ray is an angle bisector (definition of angle bisector).