Math, asked by py962117, 2 days ago

prove that a diagonal divides a parallelogram into two congruent triangles ​

Answers

Answered by XxEVILxspiritxX
1

consider Δ ABC and Δ ACD

Since the line segments AB+CD are parallel

to each other and AC is a transversal

∠ ACB = ∠ CAD.

AC = AC (common side)

∠CAB = ∠ ACD.

Thus, by ASA criteria

ΔABC ≅ ΔACD

The corresponding part of the congruent

triangle are congruent

AB = CD + AD = BC

Answered by niranjanapradeep
1

Step-by-step explanation:

Consider a parallelogram ABCD with diagonal AC.

Now in Triangle ABC & CDA

AB =DC (opposite sides of a parallelogram)

AD=BC (opposite sides of a parallelogram)

AC = AC (common)

Therefore,

by SSS rule,

Triangle ABC congruent to triangle CDA

Hence proved

Similar questions