Answer:
Given
For the Δ ACB
AC≅BC
∠ADB≅∠BEA
To prove AE≅BD
Solution:
Proof:
Statement Reason
1) AC≅BC Given
2) Δ ACB is an isosceles triangle By definition of isosceles triangle (Triangle with two sides congruent)
3) ∠CAB≅∠CBA By isosceles triangle theorem (The angles opposite to the
congruent sides are congruent.
4) ∠DAB≅∠EBA Angles with same measures
5) ∠ADB≅∠BEA Given
6) AB≅AB Reflexive property (the segment is congruent to itself.
7) ΔADB≅ΔBEA A.A.S.(Angle Angle Side)
8) AE≅BD Corresponding parts of congruent triangles are congruent.
Hence proved.
