Prove that a diagonal of a parallelogram divides it into two congruent

1.	Prove that a diagonal of a parallelogram divides it into two congruent triangles
Answer» 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.

Prove that a diagonal of a parallelogram divides it into two congruent triangles

Answer»

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.