Question

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

Answer 1

To show that quadrilateral ABCD is a parallelogram, we need to prove that its opposite sides are parallel. Given that triangle ADC is congruent to triangle CBA, we know that angle ADC is congruent to angle CBA and angle CDA is congruent to angle ACB. Using these congruent angles, we can conclude that AD is parallel to BC and CD is parallel to AB. Hence, ABCD is a parallelogram.

Step-by-step explanation:

To show that quadrilateral ABCD is a parallelogram, we need to prove that its opposite sides are parallel.

Given that triangle ADC is congruent to triangle CBA, we know that angle ADC is congruent to angle CBA and angle CDA is congruent to angle ACB.

Using these congruent angles, we can conclude that AD is parallel to BC and CD is parallel to AB. Hence, ABCD is a parallelogram.