TwiddleLab / Courses / Math
Shapes and Proof
Cut, slide and rearrange shapes until you can prove why the rules are true.
Best after: Algebra in Motion
Lessons
- Why Triangles Add to 180 (5 min): The three angles of any triangle add to 180°.
- Same Shape, Same Size (7 min): Three side lengths fix a triangle: it cannot change shape. A square can.
- Similar Triangles and Shadows (7 min): Similar triangles have the same angles; every side is multiplied by the same scale factor.
- Pythagoras by Rearranging (7 min): In a right triangle, a² + b² = c², where c is the long side opposite the right angle.
- Proof as a Chain (7 min): A proof is a chain: every link follows from what is given or from links above it.
- Circles and Angles (7 min): An inscribed angle (corner on the circle) is half the central angle on the same arc.
- Area by Cutting and Sliding (7 min): Cutting a shape and moving the pieces keeps its area: a parallelogram is base × height.
- Coordinates Meet Geometry (7 min): The distance between two points is the hypotenuse of the right triangle between them: d = √(dx² + dy²).
- Constructions (7 min): A construction uses only a compass (equal distances) and a straight edge (lines through two points).
- Project: Prove It Yourself (8 min): Testing a few shapes makes a claim convincing; only a chain of reasons makes it proved.
Lessons are interactive and need JavaScript. Turn it on to play them.
