Question

Show that a diagonal of a parallelogram divides into two congruent triangles and hence prove that the opposite sides of a parallelogram are equal.

Answer 1

REF. Image.

consider $\Delta$ ABC and $\Delta$ ACD

Since the line segments AB+CD are parallel

to each other and AC is a transversal

$\angle$ ACB = $\angle$ CAD.

AC = AC (common side)

$\angle$CAB = $\angle$ ACD.

Thus, by ASA criteria

$\Delta$ABC $\cong$ $\Delta$ACD

The corresponding part of the congruent

triangle are congruent

AB = CD + AD = BC