Question

from unit 2, lesson 13 in quadrilateral abcd, triangle adc is congruent to triangle cba. show that quadrilateral abcd is a parallelogram.

Explanation:

Step1: Recall congruent - triangle properties

Since $\triangle ADC\cong\triangle CBA$, corresponding sides are equal. That is, $AD = CB$ and $DC=BA$.

Step2: Apply parallelogram definition

A quadrilateral is a parallelogram if both pairs of opposite sides are equal. In quadrilateral $ABCD$, we have $AD = CB$ and $DC = BA$. So, $ABCD$ is a parallelogram.

Answer:

Quadrilateral $ABCD$ is a parallelogram because when $\triangle ADC\cong\triangle CBA$, the opposite - sides of the quadrilateral ($AD$ and $CB$, $DC$ and $BA$) are equal, which satisfies the definition of a parallelogram.