Level 4: Angle facts

Geometry · level 4 of 8 · rough age 11-12 (a guide for parents; anyone can start anywhere)

In level 3 you measured angles. In this level you work them out exactly, without a protractor, and you learn why each fact is true. A handful of facts (straight lines, crossing lines, parallel lines) lock together to prove that a triangle's angles add to 180°, to find the angles of any polygon, and to show why only three regular shapes can tile a floor. The level ends with symmetry by turning.

Lesson	You will be able to
Angles on a straight line and around a point	Find missing angles using 180° and 360°, and solve angle equations with letters
Vertically opposite angles	Prove that opposite angles at a crossing are equal, and use it to find all four angles from one
Angles in a triangle add to 180°	Show the 180° fact three ways, and use it and the exterior angle fact to find missing angles
Angles with parallel lines	Use corresponding, alternate and co-interior angles, and follow Euclid's proof of the 180° fact
Angles inside and outside any polygon	Find the angle sum of any polygon, the angles of any regular polygon, and explain why only three regular polygons tile
Rotational symmetry	Find the order and angle of rotational symmetry of a shape, and tell it apart from line symmetry

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