Answer:
See Below.
Step-by-step explanation:
Please refer to the attachment below.
Essentially, we want to prove that AE bisects ∠A.
Statements: Reasons:
[tex]1)\text{ } \Delta ABC \text{ is isosceles}[/tex] Given
[tex]2)\text{ } m\angle C=m\angle B[/tex] Isosceles Triangle Theorem
[tex]3)\text{ }m\angle C=m\angle ACE+m\angle ECD[/tex] Angle Addition
[tex]4)\text{ } CE\text{ bisects }\angle C[/tex] Given
[tex]5)\text{ } m\angle ACE=m\angle ECD[/tex] Definition of Bisector
[tex]6)\text{ } m\angle C=2m\angle ECD[/tex] Substitution
[tex]7)\text{ } m\angle B=\angle ABE+m\angle EBD[/tex] Angle Addition
[tex]8)\text{ } BE\text{ bisects } \angle B[/tex] Given
[tex]9)\text{ }m\angle ABE=m\angle EBD[/tex] Definition of Bisector
[tex]10)\text{ } m\angle B=2m\angle EBD[/tex] Substitution
[tex]11)\text{ } 2m\angle ECD=m\angle EBD[/tex] Substitution
[tex]12)\text{ } m\angle ECD=m\angle EBD[/tex] Division Property of Equality
[tex]13)\text{ } CE=BE[/tex] Isosceles Triangle Theorem
[tex]14)\text{ } AC=AB[/tex] Isosceles Triangle Theorem
[tex]15)\text{ } AE=AE[/tex] Reflexive Property
[tex]16)\text{ } \Delta AEC\cong \Delta AEB[/tex] SSS Congruence
[tex]17)\text{ } \angle CAE\cong \angle BAE[/tex] CPCTC
[tex]18)\text{ } AE\text{ is a bisector of } \angle A[/tex] Converse of Bisector
