Question

Prove that the diagonal of parallelogram divides it into two congruent triangle

Answer 1

GIVEN

ABCD is parallelogram

PROVE

TRIANGLE ABC CONGRUENT TO TRIANGLE ADC

PROOF

In ABC & ADC

AB =CD (OPP SIDES OF //grm)

AD =BC (OPP SIDES OF // grm )

AC=AC (COMMON)

TRIANGLE ABC CONGRUENT TO TRIANGLE ADC (BY SSS RULE)

HENCE PROVED

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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