Question

a diagonal of parallelogram divides it into two congruent triangle

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Answer 1

$\huge{Answer}$

Parallelogram Theorem #1: Each diagonal of a parallelogram divides the parallelogram into two congruent triangles.

Parallelogram Theorem #2: The opposite sides of a parallelogram are congruent. ... You can show that alternate interior angles are congruent and hence lines are parallel for this part of the proof.

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