SOLUTION: Given: X is the midpoint of WY and VZ. Proven: VW=ZY what are the reasons and statement of this? I do not understand.

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Question 1125971: Given: X is the midpoint of WY and VZ.
Proven: VW=ZY
what are the reasons and statement of this? I do not understand.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
if x is the midpoint of vz and wy, then the two lines must intersect at x.

if you then draw line between vw and zy, you have two triangles that are congruent to each together.

as such, the corresponding sides are congruent.

here's my diagram.

$$$

wy and vz intersect at x.
draw lines wz and vy.
since x is the midpoint of wy, then wx = xy.
since x is the midpoint of vz, then vx = xz.
angles wxz and vxy are congruent because they are vertical angles.
triangles wxz and vxy are congruent by SAS.
wz is congruent to vy because they are corresonoding sides of congruent triangles.