Given: in quadrilateral wxyz , `bar(wy)` and `bar(xz)` bisect each other at point a. prove: quadrilateral wxyz is a parallelogram.

Consider the quadrilateral WXYZ, it is given that the diagonals bisect each other that means ZO = OX and WO = OY.

To prove: The quadrilateral WXYZ is a parallelogram.

Proof:

Consider the triangles ZOY and WOX,

Here, OZ = OX

WO = OY

(Vertically opposite angles)

Therefore, By SAS criteria

Therefore, ZY = WX and (By Cpct)

Consider the triangles ZOW and YOX,

Here, OZ = OX

WO = OY

(Vertically opposite angles)

Therefore, By SAS criteria

Therefore, ZW = YX and (By Cpct)

Therefore, now we get ZY=WX , ZW=YX that is opposite sides of the given quadrilateral are equal.

Since,

Consider

Now, consider  

Hence, opposite angles of the given quadrilateral are equal.

Hence, the given quadrilateral is a parallelogram.

d

step-by-step explanation:

d

4+n=5

step-by-step explanation:

this is because the four is four hours and the n represents the 1 extra hour over the weekend.

b= i'm srry i don't know that one.

4+n=5 n=1 because if vernon plays 5 hours a week then 4+1=5 hours.

hope this : )