Question

Given BD bisects ∠ABC, complete the flowchart proof below. Note that the last statement and reason have both been filled in for you.

Answer 1

In order to prove that the triangles are congruent, we can write the following statements and reasons:

first box in the first row:

statement: BD bisects angle ABC

reason: given

first box in the second row:

statement: angle ABD congruent to angle DBC

reason: A segment bisector divides a segment into two congruent segments.

second box in the second row:

statement: angle ADB congruent to angle BDC

reason: given

third box in the second row:

statement: side AB congruent to side BC

reason: given

Since we have two pairs of congruent angles and one pair of congruent sides that are not between the angles, we can prove the triangles congruent by case AAS.