# Bishop's Paradise

Weekly Problem 37 - 2013

Which of the statements about diagonals of polygons is false?

Which of the statements about diagonals of polygons is false?

## Problem

Which of the following statements is false?

A An octagon has $20$ diagonals

B A hexagon has $9$ diagonals

C A hexagon has $4$ more diagonals than a pentagon

D A pentagon has the same number of diagonals as it has sides

E A quadrilateral has twice as many diagonals as it has sides

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

## Student Solutions

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This can be used to show that A to D are all correct. A quadrilateral has half as many diagonals as it has sides, not twice as many, so statement E is false.

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