Question

Given BD(line over 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 of the first row:

Statement: BD bisects angle ABC

Reason: Given

First box of the second row:

Statement: Angle ABD congruent to angle DBC

Reason: Definition of angle bisector

Second box of the second row:

Statement: angle ADB congruent to angle BDC

Reason: Given

Third box of the second row:

Statement: Side AB congruent to side BC

Reason: Given

Since we have two pair of corresponding angles and one pair of corresponding sides congruent, the triangles are congruent by case AAS.