Question

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

Answer 1

Here is your solution

Given:-

A parallelogram ABCD and AC is its diagonal .

To prove :-

△ABC ≅ △CDA

Proof :-

In △ABC and △CDA,
we have 

∠DAC =  ∠BCA [alt. int. angles, since AD | | BC] 

AC = AC [common side] 

And

∠BAC = ∠DAC [alt. int. angles,since AB | | DC]  

∴ By
ASA congruence axiom, we have 

△ABC ≅ △CDA

Hope it helps you

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.