Question

Quadrilateral ABC has opposite sides that are parallel and side AB congruent to side DC. What classification can be given to ABCD

Answer 1

Both pairs of opposite sides are parallel.
There is a quadrilateral whose definition is exactly that.
Do you know which quadrilateral that is?

Answer 2

Parallelogram

Answer 3

Correct. From the two pairs of parallel opposite sides, we know it's a parallelogram.

Now let's look at the second piece of information.
Sides AB and DC are congruent.

Answer 4

In a parallelogram, opposite sides are congruent.
This information does not add anything to what we already knew, so the conclusion is that polygon ABCD is a parallelogram.

Answer 5

Thanks for your help

Answer 6

If two adjacent sides were congruent, such as sides AB and BC, then all sides would be congruent, and we would be able to conclude it's a rhombus. This is not the case, so all we know is it's a parallelogram.

Answer 7

You're welcome.