Chapter 4.6, Problem 37PPS

To determine

To Prove:

Two column proof of theorem $4.11$ .

Explanation of Solution

Proof:

Converse of isosceles triangle theorem states that “if two angles are congruent then the sides opposite those angles are congruent”.

It is given that,

  $\angle B\cong \angle C$ .

  

  $\overline{AB}\cong \overline{AC}$

In case two angles and the non included side ofone triangle are congruent to the corresponding two angles and side of a second triangle, then the two triangles are congruent.

Corresponding parts of congruent triangles are congruent.

Statements	Reasons
Let, $\overline{AD}$ bisect $\angle BAC$	Construction
$\angle BAD\cong \angle DAC$	Definition of angle bisector
$\angle B\cong \angle C$	Given
$\overline{AD}\cong \overline{AD}$	Reflexive property of congruence
$△ABD\cong △ACD$	AAS postulate theorem.
$\overline{AB}\cong \overline{AC}$	Corresponding parts of congruent triangles are congruent.