Answer:
See Below.
Step-by-step explanation:
Please refer to the attachment below.
In order to complete the proof, we create a new segment DE that extends from D and is equal to AD. The endpoint of DE will be connected to B.
Statements: Reasons:
[tex]1)\text{ } AD\text{ bisects } CB[/tex] Given
[tex]2)\text{ } CD=DB[/tex] Definition of Bisector
[tex]3)\text{ } AE=DE[/tex] Given
[tex]4)\text{ } \angle ADC \cong \angle EDB[/tex] Vertical Angles are Congruent
[tex]5)\text{ } \Delta ADC\cong \Delta EDB[/tex] SAS Congruence
[tex]6)\text{ } \angle BED\cong \angle CAD[/tex] CPCTC
[tex]7)\text{ } AD\text{ bisects } \angle A[/tex] Given
[tex]8)\text{ } \angle CAD\cong \angle BAD[/tex] Definition of Congruence
[tex]9)\text{ } \angle BED\cong\angle BAD[/tex] Substitute
[tex]10)\text{ } BE=BA[/tex] Isosceles Triangle Theorem
[tex]11) \text{ } BE=CA[/tex] CPCTC
[tex]12)\text{ } CA=BA[/tex] Substitute
[tex]13)\text{ } \Delta ABC\text{ is isosceles}[/tex] Isosceles Triangle Definition
