Question

For the given trapezoid ABCD, triangles DAB and CBA are congruent, which of the following statement is true?

• A. $BD\cong CD$
• B. $\angle BCE\cong \angle DAB$
• C. $DA\cong DC$
• D. $\angle ACB\cong \angle BDA$

Answer 1

The correct option is D $\angle ACB\cong \angle BDA$

Given that $△ABC$ and $△ABD$ are congruent.

Which means corresponding sides and angles are equal/congruent.

$AD\cong BC,AC\cong BD,AB$ is a common side

$\angle BAD\cong \angle ABC,\angle ADB\cong \angle ACB,\angle ABD\cong \angle BAC$

Hence, the answer is $\angle ACB\cong \angle BDA$.