In the figure below, XW is the perpendicular bisector of YZ. Which one of the following is not necessarily true?

A. triangle XYZ is equiangular
B. W is the midpoint of YZ
C. triangle XYW = triangle XZW
D. triangle XYZ is isosceles

Image: http://bluejay.cty.jhu.edu/file.php/105/6418_4b02ac8e/image006.gif

Question

In the figure below, XW is the perpendicular bisector of YZ. Which one of the following is not necessarily true?

A. triangle XYZ is equiangular	
	 B. W is the midpoint of YZ	
	 C. triangle XYW = triangle XZW	
	 D. triangle XYZ is isosceles

Image: http://bluejay.cty.jhu.edu/file.php/105/6418_4b02ac8e/image006.gif

anonymous · Answer

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directrix · Answer

XW is the perpendicular bisector of YZ
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All points on the perpendicular bisector of a segment are equidistant from the endpoints of the segment.  So XY = XZ

directrix · Answer

W has to be the midpoint of segment YZ because segment XW bisects segment YZ.

directrix · Answer

@they_said_hi   What are you thinking would be or might be the option that is not necessarily true?

directrix · Answer

Two options have been eliminated.

anonymous · Answer

It looks like the answer is  A. [triangle XYZ is equiangular] -- since nowhere in the def. of perpendicular bisectors does it even mention equiangularity; we can't prove that, but we can prove everything else.

directrix · Answer

That is correct.