Compass & Straightedge · ConstructLab

Construction puzzles

The ancient Greeks constructed with just two tools: a compass (circle centred at one point through another) and an unmarked straightedge (line through two points).

Pick a tool, then click two existing points. New intersections appear automatically and you can build on them.

Reach the goal in as few moves as possible to earn three stars.

Replay

Each level's shortest construction, replayed step by step like a video. Drag the timeline to stop at any step and see where every point comes from.

Congruence test

Two triangles that can be made to coincide exactly are congruent. You don't need all six parts equal; any of these is enough: SSS, SAS, ASA, AAS, and HL for right triangles.

Drag the vertices of the left triangle, then press Overlay: the right triangle is reflected, rotated and translated onto it.

The last option, SSA, is a counterexample: two sides and a non-included angle do not guarantee congruence.

Similarity & homothety

Scale every point's distance from a centre O by k: the result is a homothetic image, and O is the centre of homothety.

Homothetic figures are similar: every pair of sides has ratio |k|, so does the perimeter, and the area ratio is k².

Drag O and the vertices, or change k.