Question

Statements and Reasons from the photo above

Answer 1

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.