Question

does a diagonal of a parallelogram divide the parallelogram into two congruent triangles? If yes, state the condition of congruency. ​

Answer 1

Step-by-step explanation:

The diagram for the question is as below:

Diagonal AC divides the parallelogram into two triangles △ABC and △ADC.

In △ABC and △ADC:

∵ AD||BC

∠BAC = ∠DCA ( By alternate angle)

AC = AC (Common side)

∠BCA = ∠DAC ( By alternate angle)

In these two triangles, one side and two angles made on this side are equal.

Therefore by ASA rule of congruence:

△ABC ≅ △ADC.

Since, both these triangles are congruent. So, all the corresponding sides and angles of one triangle are equal to that of the other.

∴ AD= BC

And AB = CD.

Therefore, it is proved that the diagonal of a parallelogram divides it into two congruent triangles and also opposite sides of a parallelogram are equal.