Quadrilateral ABCD is shown in the illustration. Prove that ABCD is a parallelogram with opposite sides that are congruent.

Drag and drop the statements to correctly compete the sentence.

The coordinates of point C are (a+b, c).

AD = BC=b2+c2−−−−−−√ .

AB = DC= Response area.

The slope of ​ AD¯¯¯¯¯ ​ and ​ BC¯¯¯¯¯ ​ is Response area.

The slope of AB and DC is Response area.

By the definition of congruence, AD¯¯¯¯¯≅BC¯¯¯¯¯ and AB¯¯¯¯¯≅DC¯¯¯¯¯.

Since Response area, AD¯¯¯¯¯∥BC¯¯¯¯¯ and AB¯¯¯¯¯∥DC¯¯¯¯¯.

Therefore, the opposite sides are parallel and congruent.