Question

based on the information given, can you determine the quadrilateral must be a parallelogram? explain

Answer 1

given line XN~NZ and line NY~NW

Answer 2

@DemolisionWolf

Answer 3

the ~ sign means the equal sign with ~ above it i didnt know how to type it on the keyboard

Answer 4

ok, i understand

Answer 5

hmm... I don'[t feel like i'm all that great at doing proof-like questions...

Answer 6

well do you know how to possibly get me on the right track for this one? i think it is a parallelogram, but im not sure and dont know how to explain it

Answer 7

it is a parallelogram. it is because the top and bottom are parallel, and the sides are parallel also, then the diagonal lengths given just confirm this....

Answer 8

@ranga can you look at this when you get a chance?

Answer 9

NX = NZ (given)
NW = NY (given)
angle XNW = angle YNZ (vertical opposite angles)
Triangles XNW and ZNY are congruent (by SAS)
Therefore, angle NXW = angle NZY and angle NWX = angle NYZ
But NXW and NZY are alternate interior angles.
Also, NWX and NYZ are alternate interior angles.
Therefore, WX and ZY must be parallel.
Similarly, you can prove XY and WZ are parallel.

Therefore, WZYX is a parallelogram.