Question

GIVEN: AD is angle bisector of

Answer 1

Given:

AD is angle bisector of angle BAC.

AB = AC.

The objective is to prove BD = DC.

Step 1:

Statement: AD is angle bisector of angle BAC.

Reason: Given.

Step 2:

Statement:

$\angle BAD=\angle\text{DAC}$

Reason: Definition of angle bisector.

Step 3:

Statement:

$AB\cong AC$

Reason: Given

Step 4:

Statement: AD = AD.

Reason: Reflexive.

Step 5:

Statement:

$\Delta BAD\text{ }\cong\text{ }\Delta CAD$

Reason: By SAS criteria.

Step 6:

Statement:

$BD\cong DC$

Reason: By Corresponding parts of congruent triangles (CPCT).

Hence, the required results are obtained.