SOLUTION: I have a proof and shown is quadrilateral ABCD. On the figure the diagonals AC and DB are drawn. The point where they intersect is marked X. The givens are that AB and DC are paral

Algebra ->  Geometry-proofs -> SOLUTION: I have a proof and shown is quadrilateral ABCD. On the figure the diagonals AC and DB are drawn. The point where they intersect is marked X. The givens are that AB and DC are paral      Log On


   

Question 242229: I have a proof and shown is quadrilateral ABCD. On the figure the diagonals AC and DB are drawn. The point where they intersect is marked X. The givens are that AB and DC are parallel and that AC bisects BD. And I need to prove that figure ABCD is a parallelogram. I also need to set it up in the standard proof column order with statements on one side and reasons on the other. Thank you!
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!

I have to use equal signs because the congruence symbol won't render. The strategy is to prove one pair of opposite sides both parallel and congruent -- parallel because given and congruent because CPCTC


Given

Opposite interiors

Vertical angles

Definition of a bisector

ASA

CPCTC

is a parallelogram. Two opposite sides are both parallel and congruent.



John