Ariel wrote a paragraph proof to prove that the diagonals of parallelogram MNOP bisect each other. Drag and drop the statements and reasons of her proof to put them in the correct order, starting with the first step at the top.
1.when I think of the diagonals as transversals cutting parallel lines, I can see that <mop =<omn and <npo=<pnm because of the alternate interior angles theorem
2.By the cpctc theorem, I know that ML = OL and NL=PL MO=NP bisect each other other because this is the definition of a bisector.
3.Because of the definition of a parallelogram, I know that the opposite sides are congruent. I can say that MN=OP. I know have enough information to say that MNL=OPL by the ASA congruence theorem.
4.I am given that quadrilateral MNOP is a parallelogram. I know that opposite sides of a parallelogram are congruent because of the definition of a parallelogram, so MN || NO.
1. Because of the definition of a parallelogram, I know that the opposite sides are congruent. I can say that MN = OP. I now have enough information to say that ∠MNL = ∠OPL by the ASA congruence theorem.
2. I am given that quadrilateral MNOP is a parallelogram. I know that opposite sides of a parallelogram are congruent because of the definition of a parallelogram, so MN ∥ NO.
3. When I think of the diagonals as transversals cutting parallel lines, I can see that ∠MOP = ∠OMN and ∠NPO = ∠PNM because of the alternate interior angles theorem.
4. By the CPCTC theorem, I know that ML = OL and NL = PL. MO = NP bisect each other because this is the definition of a bisector.