Question

In the adjacent figure, seg AD ≌ seg EC Which additional information is needed to show that ∆ ABD and ∆ EBC will be congruent by A-A-S test ?

Answer 1

In ∆ABD and ∆EBC,

side AD ≅ side EC (given)
∠ABD ≅ ∠EBC (vertically opposite angles)

∴ To show that ∆ ABD and ∆ EBC will be congruent by A-A-S test, one of the following is needed:
∠BAD ≅ ∠BCE
or
∠BDA ≅ ∠BEC.