Question

Prove that the diagonals of a parallelogram will divide the parallelogram in two congruent triangles ​

Answer 1

Answer:

A diagonal of a parallelogram divides it into two congruent triangles. Given : A parallelogram ABCD. Construction : Draw a diagonal AC. Hence, it is proved.

Answer 2

Step-by-step explanation:

To Prove :-

Diagonal of a parallelogram divide it into two congruent triangles .

• Solution :-

Given :-

ABCD is a parallelogram . AC is the diagonal .

To prove :-

∆ ADC congruent to ∆ ABC

Proof :-

Opposite sides of a parallelogram are parallel to each other . So,

DC || AB

AD is transverse line . So,

Angle DAC = Angle ACB .

Angle DCA = Angle CAB

In triangle ADC and triangle ABC

AD = AD. ( common )

Angle DAC = Angle ACB ( Proved above)

Angle DCA = Angle CAB ( Proved above)

By ASA criteria .

∆ ADC is congruent ∆ ABC .

Hence proved