Question

Katie draws two chords in a circle in a certain way. She then draws in four segments between adjacent endpoints of the chords to form a quadrilateral. Which of the following is not true about the chords if Katie constructed a square?

A. The chords must both be diameters.
B. The chords must bisect one another.
C. The chords must be perpendicular to one another.
D. The chords must form two acute and two obtuse angles at their intersection.

Answer 1

Answer: The answer that is not true is choice D.

If Katie drew those chords and those line segments to form a square, then the diagonals would have to be congruent. The only way to have them would be through the center, therefore they must be diameters.

And if it is a square, then the diagonals are perpendicular bisectors meaning the angles would be right angles not acute or obtuse as in Choice D.