Question

Q.no 2 .Prove that in parallelogram ABCD,the diagonal AC divides the parallelogram into two congruent triangles.

Answer 1

In a ||gm Opposite sides are equal so when a diagonal divide it into two parts it is said it is a congurent triangle....

Answer 2

Statement : A diagonal of a parallelogram divides it into two congruent triangles.

Given : A parallelogram ABCD.

To prove : ΔBAC ≅ ΔDCA

Construction : Draw a diagonal AC.

Proof :

In ΔBAC and ΔDCA,

∠1 = ∠2 [alternate interior angles]
∠3 = ∠4 [alternate interior angles]
AC = AC [common]

ΔBAC ≅ ΔDCA [ASA]

Hence, it is proved.