1. Polygons Decide which of these are true and which are false.
[GM1.1 Core Plenary]
Decide which of these are true and which are false.
Be prepared to justify your answers!
It is impossible to draw an octagon with four acute interior angles.
A hexagon can have two interior angles which are reflex.
There isn’t a regular polygon whose interior angles are 155°.
The interior angles of regular polygons are usually whole numbers of degrees.
Only regular polygons with even numbers of sides have pairs of sides which are parallel.
Preamble
The five statements to test are suitable for pairs. Some pupils might not consider reflex polygons as being polygons. Encourage pupils, with the obvious caveats, to challenge each other’s reasons and stress that it is the reason(s) which are important and that they must be able to support their answers.
Possible content
Names of regular polygons and their internal angles; recognising acute and reflex angles.
Resources
None.
Solution/Notes
False, for example
True, for example
True, external angle is 360 ÷ (180 – 155) which is 14.4 “sides” so not possible.
Not true; there are some fractional interior angles however from triangle to 20-gon only 7 have non-integer angles.
True.
Original Material © Cambridge University Press 2010
Original Material © Cambridge University Press 2010