8.1 Polygons · Unit 8 Shapes and symmetry

1 · Teaching slidesuse ← → keys

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2 · Key words

polygonA closed shape made of straight sides.

regular polygonAll sides equal and all angles equal.

vertexA corner where two sides meet.

interior angleAn angle inside the polygon at a vertex.

exterior angleThe angle between a side and the extension of the next side.

angle sumThe total of the interior angles: 180(n − 2)°.

pentagonA five-sided polygon.

hexagonA six-sided polygon.

octagonAn eight-sided polygon.

3 · Summary of the sectionrevise from this

A polygon is a closed shape with straight sides. It is regular only if the sides and the angles are all equal.
The interior angles of an n-sided polygon total 180(n − 2)° — it splits into n − 2 triangles.
For a regular polygon, each interior angle is 180(n − 2) ÷ n.
The exterior angles of any polygon total 360°, whatever the number of sides.
So each exterior angle of a regular n-gon is 360 ÷ n.
An interior angle and its exterior angle lie on a straight line, so they add to 180°.
Going through the exterior angle is usually the quicker route: one fixed total and one division.
If 360 ÷ (exterior angle) is not a whole number, no such regular polygon exists.

PDFPrintable worksheet All 68 questions, space to work PDFWorked answers Full solutions, not just the answer

Video lessons2 videos

Math Antics - Polygons

American mathantics

What counts as a polygon, the names, and regular versus irregular.

Math Antics - Quadrilaterals

American mathantics

The four-sided family in detail — a useful bridge from Unit 5.

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Polygons