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**sydbernard**- Replies: 1

1. For which numbers n can it happen that a (not necessarily convex) pentagon has exactly n diagonals lying entirely in its interior? For each possible n, draw an example of a pentagon with exactly that many such “internal diagonals”.

2. Can a convex broken line self-intersect? (If yes, give an example, if no, give a proof.)

Thank you!

**sydbernard**- Replies: 4

Give an example that disproves the proposition “If the bisectors of two angles with a common vertex are perpendicular, then the angles are supplementary.” Is the converse proposition true? I've only been able to come up with examples that prove this proposition and can't think of any that show it's false.

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