Geometry
From angle chasing to 3-D solids and coordinates, figures you can move.
- 29Angle ChasingreadyStraight lines, triangles, parallels, polygons and circles: five simple angle rules that, chained together, crack surprisingly hard contest problems.
0% - 30Triangle Area and LengthreadyOne triangle, five area formulas (base-height, Heron, rs, abc/4R, shoelace) plus Pick's theorem, medians, centroids and Stewart's theorem for every cevian.
0% - 31Special TrianglesreadyEquilateral, 45-45-90, 30-60-90 and 13-14-15 triangles plus a handful of Pythagorean triples: learn their ratios once and most right-triangle problems become arithmetic.
0% - 32Similar TrianglesreadySame shape, different size: spot two equal angles and every length scales by k, every area by k². Plus the right-triangle altitude facts and the Angle Bisector Theorem.
0% - 33QuadrilateralsreadySquares, rectangles, rhombi, parallelograms and trapezoids: their area formulas, what their diagonals do, and how to cut any quadrilateral into triangles you can handle.
0% - 34CirclesreadySlices, crusts and touching circles: sectors and arcs, radii that turn tangent circles into right triangles, the power of a point, and the special rules of quadrilaterals inscribed in a circle.
0% - 35PolygonsreadyRegular hexagons, octagons and pentagons hide simpler shapes inside: six equilateral triangles, a square with its corners cut off, and the golden ratio.
0% - 363-D GeometryreadyCubes, boxes, cylinders, cones, spheres and pyramids: their volume and surface-area formulas, space diagonals and slant heights, and the big trick for 3-D problems: slice through the centers and solve a 2-D picture.
0% - 37Area and Length of Complex ShapesreadyNo formula for a strange shape? Build one: add the pieces you know, subtract the ones you don't, extend lines and drop altitudes until every area and length is a sum of easy parts.
0% - 38Coordinate GeometryreadyPut the picture on a grid: lines become equations, lengths become square roots, and any polygon's area comes from the shoelace formula or Pick's theorem.
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