4. Prove that a diagonal of a parallelogram divides it into two congru

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

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

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