Level 5: Constructions and transformations

Geometry · level 5 of 8 · rough age 12-13 (a guide for parents; anyone can start anywhere)

At this level geometry stops being only about looking and starts being about reasons. You build exact figures with a compass and an unmarked ruler, and find out which triangles can exist at all. You move shapes around the whole coordinate grid by sliding, flipping, turning and scaling them. Then you learn the five tests that prove two triangles are exact copies, and use them to explain the facts about circles.

Lesson	You will be able to
1. Compass and straightedge	Copy a segment, bisect a segment and an angle, build 60°, 30°, 45° and 90° exactly, and explain why each recipe works
2. Constructing triangles	Construct a triangle from three sides or from sides and angles, and use the triangle inequality to tell when no triangle exists
3. Transformations on the grid	Translate, reflect and rotate shapes in all four quadrants with coordinate rules, and say why the rules work
4. Dilations and scale drawings	Enlarge and reduce shapes from a centre, read maps and blueprints, and know why areas scale by \(k^2\)
5. Congruent triangles	Use SSS, SAS, ASA, AAS and RHS to prove triangles congruent, and show why SSA and AAA fail
6. Circle words	Name every part of a circle and prove the facts about chords, tangents and radii

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