Question

If ABCD is a parallelogram with AB || CD, AD || BC, and BD is the diagonal, then the $△ABD$ and $△BCD$ are always .

• A. equilateral
• B. isoceles
• C. scalene
• D. congruent

Answer 1

The correct option is D congruent


Given a parallelogram ABCD.

Consider $△ABD$ and $△BCD$.
$AB=CD$ (Opposite sides of a parallelogram are equal)
$BD=BD$ (Common Side)
$\angle ABD=\angle BDC$ (Alternate interior angles)

By SAS congruence criterion, the two triangles are congruent.