Plane Geometry

• Mathematics · Plane Geometry Triangle inequality – joining three segments 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 sliders or drag... Ages 12–13
• Mathematics · Plane Geometry Law of Cosines, Law of Sines, and triangle area Triangle ABC is built from two sides a, b and the included angle C; drag any of the three vertices freely. Every side and angle updates... Ages 15–16
• Mathematics · Plane Geometry Constructing triangles with a compass – congruence criteria Construct triangle ABC step by step as if using a ruler and compass: the SSS case (three sides), the SAS case (two sides and the... Ages 12–13
• Mathematics · Plane Geometry Circles – chords and tangents 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 that OH ⟂ AB and AB... Ages 14–15
• Mathematics · Plane Geometry Parallel Lines and a Transversal – Alternate and Corresponding Angles 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 tilt it or make it... Ages 12–13
• Mathematics · Plane Geometry Angles – protractor and midpoint Two rays Ox and Oy pivot around vertex O to form angle xOy; a semicircular protractor lines up with ray Ox so you can read the measure.... Ages 11–12
• Mathematics · Plane Geometry Lines of symmetry and point symmetry Choose a square, rectangle, rhombus, regular hexagon, or any quadrilateral, and the simulation finds and draws every line of symmetry... Ages 11–12
• Mathematics · Plane Geometry Circumscribed and inscribed circles of triangles and regular polygons Drag the three vertices of a triangle: the circumcenter O is the intersection of the three perpendicular bisectors, the incenter I is... Ages 14–15
• Mathematics · Plane Geometry Similar triangles – measuring height with shadows 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 change the ratio and... Ages 13–14
• Mathematics · Plane Geometry Thales' theorem – parallel lines in a triangle 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 AD/DB = AE/EC and... Ages 13–14
• Mathematics · Plane Geometry Quadrilaterals – identifying special shapes Drag the four vertices A, B, C, D on the grid; the simulation measures the sides, angles, and diagonals to identify a trapezoid,... Ages 13–14

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