Question

Given BD is the angle bisector of ABC complete the flowchart proof below Note that the last statement and reason have both been filled in for you

Answer 1

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.

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.