Plane Geometry

Construct and explore plane geometry: triangles with a compass, inscribed and circumscribed circles, angles with parallel lines, similar triangles, Thales' theorem, quadrilaterals and symmetry.

19 interactive Mathematics simulations on plane geometry.

Triangle inequality – joining three segments Mathematics · Plane Geometry Three segments a, b, c form a triangle if and only if each side is shorter than the sum of the other two. Drag the... Ages 12–13
Area by cutting and rearranging – parallelogram, triangle, trapezium, rhombus, composite shapes Mathematics · Plane Geometry Drag the base, height and offset of a parallelogram, triangle or trapezium and watch it being cut and rearranged... Ages 11–12
Circumference and area of a circle – roll a wheel, rearrange sectors Mathematics · Plane Geometry Roll a wheel along a ruler to measure its circumference, record results for several radii and plot C against d to... Ages 14–15
Law of Cosines, Law of Sines, and triangle area Mathematics · Plane Geometry Triangle ABC is built from two sides a, b and the included angle C; drag any of the three vertices freely. Every... Ages 15–16
Circle theorems explorer – drag points, measure angles Mathematics · Plane Geometry Pick a circle theorem and drag points on the circle: angle at the centre, angles in the same segment, angle in a... Ages 14–15
Pythagoras' theorem – squares on the sides, proofs and applications Mathematics · Plane Geometry Drag the vertices of a triangle on a grid and compare the areas of the squares on its three sides: a² + b² = c² only... Ages 13–14
Ruler-and-compass constructions and loci – bisectors, perpendiculars and regions Mathematics · Plane Geometry Watch ruler-and-compass constructions animated step by step: the perpendicular bisector of a segment, the angle... Ages 12–13
Constructing triangles with a compass – congruence criteria Mathematics · Plane Geometry Construct triangle ABC step by step as if using a ruler and compass: the SSS case (three sides), the SAS case (two... Ages 12–13
Circles – chords and tangents Mathematics · Plane Geometry Circle (O; R) with a chord AB and an external point M. Drag the chord's midpoint H to change the distance OH and see... Ages 14–15
Parallel Lines and a Transversal – Alternate and Corresponding Angles Mathematics · Plane Geometry Two lines a and b are cut by a transversal line c at points A and B, forming 8 angles. Drag the end of line b to... Ages 12–13
Angle facts – angles at a point, parallel lines, triangle and polygon angle sums Mathematics · Plane Geometry Drag rays to explore angles on a straight line, complementary angles, vertically opposite angles and angles around a... Ages 12–13
Angles – protractor and midpoint Mathematics · Plane Geometry Two rays Ox and Oy pivot around vertex O to form angle xOy; a semicircular protractor lines up with ray Ox so you... Ages 11–12
Lines of symmetry and point symmetry Mathematics · Plane Geometry Choose a square, rectangle, rhombus, regular hexagon, or any quadrilateral, and the simulation finds and draws every... Ages 11–12
2D + 3D Similar shapes – enlargement, scale factor k, k² and k³ Mathematics · Plane Geometry Four screens on similarity. Enlargement: drag the centre O and the vertices, choose a scale factor k (including... Ages 13–14
Circumscribed and inscribed circles of triangles and regular polygons Mathematics · Plane Geometry Drag the three vertices of a triangle: the circumcenter O is the intersection of the three perpendicular bisectors,... Ages 14–15
Similar triangles – measuring height with shadows Mathematics · Plane Geometry Two similar triangles ABC and A'B'C' with ratio k: drag the vertices of ABC to reshape it, or drag B' or C' to... Ages 13–14
Thales' theorem – parallel lines in a triangle Mathematics · Plane Geometry Triangle ABC with a line DE crossing sides AB and AC. Drag D along AB (E follows so that DE ∥ BC) to see the ratios... Ages 13–14
Quadrilaterals – identifying special shapes Mathematics · Plane Geometry Drag the four vertices A, B, C, D on the grid; the simulation measures the sides, angles, and diagonals to identify... Ages 13–14
Quadrilateral explorer – identifying special quadrilaterals Mathematics · Plane Geometry Drag the four vertices A, B, C, D, or slide a whole side, on a grid of integer points; the program identifies the... Ages 13–14