Question

In quadrilateral ABCD, diagonals AC and BD bisect one another. What statement is used to prove that quadrilateral ABCD is a parallelogram?

Angles BAD and ADC are congruent.

Corresponding angles BCD and CDA are supplementary

Sides CD and DA are congruent.

Triangles BPA and DPC are congruent.

Answer 1

Here is the picture

Answer 2

I know the answer is the last one, but why is it the answer.

Answer 3

Corresponding angles BCD and CDA are supplementary

Answer 4

and it's the answer cuz i just said it

Answer 5

Do you still need help with this?

Answer 6

@boldjon it is not B...

Answer 7

You need to recall ways of proving a quadrilateral is a parallelogram.

If you follow the definition of a parallelogram, then if you prove both pairs of opposite sides are parallel, you prove the quadrilateral is a parallelogram.

Another way to prove a quadrilateral is a parallelogram is to prove that one pair of opposite sides is both parallel and congruent.

Answer 8

In choice D, if you prove the two triangles congruent, then you can prove that one pair of opposite sides of the quadrilateral is congruent because of CPCTC of the triangles, and using corresponding angles and CPCTC again, you can also prove those same two sides to be parallel. That proves the quadrilateral is a parallelogram.

Answer 9

Incidentally, the only choice that makes sense is D because all the others are not necessarily true