Quad check

[vampirewitchreine]

This is an SAT/ACT preview question, and I just want to check and see if my answer is correct


In quadrilateral WXYZ, segment WX is congruent to segment XY and segment WZ is congruent to segment ZY. What type(s) of quadrilateral can WXYZ be?
I. Kite
II. Rhombus
III. Square



The following are the answer choices:

A. I only
B. I or II
C. II or III
D. I or III
E. I, II, or III



I say that it's E.
Reasoning: Obviously, it must be no less than a kite as they have 2 congruent sets of sides. It could be a rhombus or a square as well because it doesn't specifically say that segments WX/XY and WZ/ZY aren't congruent. So there's still the possibility that all sides could be congruent to each other.

 

[srmichael]

Yes, it's E.

Be very careful when it says "CAN" versus "MUST". In this instance it CAN be a kite if WZ and ZY are of different length than WX and XY. It CAN be a rhombus if WZ and ZY are the same length as WX and XY. And it CAN be a square for the same reason as a rhombus AND if the angles are all right angles.

CAN problems are usually harder than MUST problems because you have to think of all the different options you can have in the situation given to you.