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Question

A diagonal of a paralleogram divides it into two congruent triangles.

A
True
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B
False
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Solution

The correct option is A True
Let us consider a parallelogram ABCD with AC as its diagonal.

To prove: ABCADC

Proof:

We know that the opposite sides of a parallelogram are parallel.

Hence ABDC and ADBC


AC is the transversal of the parallel lines AB and DC

BAC=DCA (Alternate angles) ...(1)


AC is the transversal of the parallel lines AD and BC

DAC=BCA ...(2)


In ABC and ADC,

BAC=DCA

AC is the common side

DAC=BCA

Therefore, ABCADC

1465959_1303911_ans_680c786888b948c19ec04eb66a1745bb.png

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