An angle is an amount of turn. This unit starts by naming and reading angles exactly, then shows that angles are not independent: those on a line add up to 180°, those at a point to 360°, and a line crossing two parallel lines makes the same angles twice. Those facts prove that the angles of every triangle add up to 180°, and the unit ends with compasses, where equal arcs build exact bisectors and triangles from three lengths.
Every idea is something you can move: open an angle through a whole turn, tilt a line across two parallels, step through a proof, change the radius of a compass arc and watch when the arcs stop meeting. Nothing needs a calculator. Every drawing is worked out exactly, not sketched.
The lessons, in order
- Lesson 1 · Points, lines and angles Points, lines, rays and segments with their notation; parallel and perpendicular; naming an angle; acute, right, obtuse, straight and reflex; reading a protractor scale. Open an angle through a whole turn, then read the same angle on both protractor scales. No calculator
- Lesson 2 · Angles on a line and at a point Angles on a straight line, angles at a point, vertically opposite angles, supplementary and complementary angles, and finding unknown angles with equations and reasons. Cross two lines and move one angle to see the other three follow; then fill the missing angle on a line or round a point. No calculator
- Lesson 3 · Parallel lines and transversals Transversals, corresponding, alternate and co-interior angles, the test for parallel lines, and finding angles with reasons. Tilt a line across two parallels to see which angle pairs stay equal; then tilt one parallel to see the equal angles disappear. No calculator
- Lesson 4 · Angles in a triangle The angle sum of a triangle, classifying triangles by angles and by sides, isosceles base angles, and finding missing angles with reasons. Lay a triangle's three corners on a straight line, then step through the parallel-line proof. No calculator
- Lesson 5 · Bisecting lines and angles Bisecting a line segment (perpendicular bisector) and an angle with compasses and a straight edge, and why the arcs must be large enough to meet. Change the compass radius to see when two arcs meet and every point on the bisector is equally far from A and B; then bisect an angle. No calculator
- Lesson 6 · Constructing triangles and angles Constructing a triangle from three sides with compasses, the condition for three lengths to make a triangle, building one from two sides and the angle between them, and constructing 60° and 30° angles. Slide two arcs to build a triangle from three sides, then step through an equilateral triangle to make 60° and bisect it to 30°. No calculator
Every lesson has a teacher page with the answers, the misconceptions each wrong answer reveals, discussion questions, differentiation and support for students learning in English, and extra questions in three tiers.