Question

In the figure AD = EC, which additional information is needed to show that $△ABD$ and $△EBC$ will be congruent by A - A - S test?

• A. $DB=EB$
• B. $\angle BAD=\angle BEC$
• C. $\angle BAD={40}^o$
• D. $AB=CB$

Answer 1

The correct option is B $\angle BAD=\angle BEC$


In $△ABDand△EBC,$
side AD = side EC (given)
$\angle ABD\cong \angle EBC$ (vertically opposite angles)
$\therefore$ To show that $△ABD$ and $△EBC$ will be congruent by A-A-S test, one of the following is needed: $\angle BAD=\angle BCE$
or
$\angle BDA=\angle BEC.$