In quadrilateral ABCD, triangle ADC is congruent to CBA. Show that ABCD is a parallelogram.

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4. In quadrilateral ABCD, triangle ADC is congruent to CBA. Show that ABCD is a parallelogram.

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Answer:To show that quadrilateral ABCD is a parallelogram, we need to prove that both pairs of opposite sides are parallel.Since triangle ADC is congruent to triangle CBA, we have: AD = CB (corresponding sides of congruent triangles are equal) DC = BA (corresponding sides of congruent triangles are equal) Since both pairs of opposite sides are equal, ABCD is a parallelogram by the definition of a parallelogram (a quadrilateral with both pairs of opposite sides equal).

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In quadrilateral ABCD, triangle ADC is congruent to CBA. Show that ABCD is a parallelogram.

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