SOLUTION: If WXYZ is a parallelogram, which of the following must ALWAYS be true? A. segment WY and segment YX bisect each other B. angle XWZ is congruent to angle XYZ C. segment WY is

Question 1104273: If WXYZ is a parallelogram, which of the following must ALWAYS be true?
A. segment WY and segment YX bisect each other
B. angle XWZ is congruent to angle XYZ
C. segment WY is perpendicular to segment ZX
D. segment WY is congruent to segment ZX
E. segment ZX bisects angle WXY

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Parallelograms (and other polygons) are named
by listing letter names of the vertices
in the order you see them as you go around the parallelogram.
So, parallelogram WXYZ would look something like this:
Line segments WY and XZ are diagonals.

A. is never true.
Diagonals bisect each other in all parallelograms,
and WY is a diagonal, that bisects diagonal XZ,
but XY is a side that meets diagonal WY and point Y,
which is an endpoint of both segments.
It is not the midpoint of either segment.

B. must always be true.
Angles XWZ and XYZ are opposite angles in WXYZ,
and opposite angles in a parallelogram are always congruent.

C. is not always true.
It is true for a rhombus
(or a square that is a special type of rhombus),
but it is not true for other parallelograms,
like the one on the figure above.

D. is not always true.
It is for a rectangle
(or a square that is a special type of rectangle),
but it is not true for other parallelograms,
like the one on the figure above.
You can see that XZ is much shorter than WY.

E. is not always true.
It is true for a rhombus
(or a square that is a special type of rhombus),
but it is not true for other parallelograms,
like the one on the figure above.
You can see that angle ZXY, measuring about
is much smaller than angle WXZ,
so those two angles adding up to angle WXY are not congruent.
RELATED QUESTIONS
If WXYZ is a parallelogram, which of the following must always be true? A. line WY and (answered by MathLover1)

given: parallelogram wxyz with diagonals segment wy and segment xz prove: p is the... (answered by ikleyn)

Theorem 3. the diagonals of a rhombus are perpendicular. Given: Rhombus ROSE Prove:... (answered by ikleyn)

what is the proof for this problem: segment BK and segment LD bisect each... (answered by Fombitz)

Help please, In what type quadrilateral are the diagonals NOT always congruent to each... (answered by stanbon)

Which is NOT always a property of a Parallelogram? A. Diagonals that bisect each other... (answered by jim_thompson5910)

bisect the segment connecting A(4,-3) and... (answered by ewatrrr)

(answered by KMST)
The vertices of a parallelogram are A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4). Which (answered by FrankM)