If a parallelogram is a cyclic quadrilateral then it is a rectangle

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Question from Kim, a student:

Show that if a parallelogram is a cyclic quadrilateral then it is a rectangle.
Hint: Observe that in a parallelogram ABCD we always have Triangle ABC is congruent to Triangle CDA.

(Would you use the diagonals in a non-rectangular parallelogram, proving that they are not of the same length, and thus it must be a rectangle?)

We have two responses for you

The hint just makes it harder -- you just have to compare the theorem that describes the opposite angles of a cyclic quadrilateral with the theorem that describes the opposite angles of a parallelogram.

Chris

Do you know the theorem that says that opposite angles in a (convex) cyclic quadrilateral sum to 180 degrees?

Good Hunting!
RD

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