Question

2. Prove that a diagnal of a Parallelogram devides
it into two congruent triangle​

Answer 1

REQUIRED ANSWER :

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