Question

a diagonal of a pallalelogram divides it into two congruent triangles proof this theorem if you know then answer otherwise don't give silly answers

Answer 1

let us consider parallelogram ABCD..
DB is a diagonal..
in triangle DBC and triangle ABD
AB =DC since parallelogram property..
BC=AD since same...
DB equals to DB
hence....
diagonal of a parallelogram divides into two congruent triangles...
hope it helps
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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.