Question

In a parallelogram that is not a rectangle or rhombus, what is the probability of 2 randomly chosen angles being congruent?

Answer 1

`1/3`

Explanation:

A parallelogram which is not a rectangle will have exactly two distinct pairs of congruent angles. Consider a parallelogram `ABCD` with angles `/_A`, `/_B`, `/_C`, and `/_D`.

Then `/_A = /_C`, `/_B=/_D` and `/_A!=/_B`

So there are two possible congruent pairs:
`(A, C), (B, D)`

and six possible pairs: `(A, B), (A, C), (A, D), (B, C), (B, D), (C, D)`

Thus the probability of randomly choosing two congruent angles is
`2/6 = 1/3`