Angles in Triangles and Polygons (including Tessellations): Probing Questions
Whether you are looking for a question to stimulate discussion in lesson, or a challenge at the end of a homework, then hopefully you will find these useful.
Contents
Convince Me That... keyboard_arrow_up
Back to Top
I use Convince Me That questions lots in my lessons and homeworks. Providing students with a statement and challenging them to come up with as many different ways of convincing you as possible can lead to some fascinating discussions. The different ways of seeing the same thing can also help improve the depth of students’ understanding. Thanks so much to the Thornleigh Maths Department, in particular Erica Richards, Anton Lewis and Gareth Fairclough for helping me put these together, and we will endeavour to keep adding more!
A triangle cannot have two obtuse angles
A triangle can have 3 acute angles.
One way of working out the total interior angles in a polygon is to get the number of sides, subtract 2, and multiply the answer by 180
Interior angle + Exterior angle = 1800
Angles in a triangle add to 1800
An exterior angle of a regular hexagon is equal to an interior angle of an equilateral triangle
There is no regular polygon which has interior angles equal in size to the exterior angles of a regular octagon.
An irregular hexagon might not have any exterior angles equal to 60o.
Angles in a pentagon must add up to 540o.
Octagons and squares tessellate, but hexagons and squares do not
VI3 Treatment keyboard_arrow_up
Back to Top
We devised VI3 Treatment as a versatile way of giving students meaningful follow-up work at once we have marked their homework. The idea is that students are challenged to come up with 3 things with certain constraints. These are ideal to use as an extension for students who have got everything correct, and also as further purposeful practise for students who have got a particular question wrong. Use the ideas below and adapt them accordingly, using different numbers where appropriate. Either mark them yourself or better still, get other students to do it. Thanks so much to the Thornleigh Maths Department, in particular Erica Richards, Anton Lewis and Gareth Fairclough for helping me put these together, and we will endeavour to keep adding more!
Draw 3 shapes which will tessellate.
Draw a labelled sketch of 3 regular polygons which have more sides than a quadrilateral.
Sketch 3 isosceles triangles that contain at least one angle of 500. Why do at least two always have to be the same triangle?