https://teddyrookbook.com/math/geometry/Recent content in Geometry on Teddy Rook Bookhttps://teddyrookbook.com/img/share.jpghttps://teddyrookbook.com/img/share.jpgHugoenhttps://teddyrookbook.com/math/geometry/points-lines-planes/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/points-lines-planes/Build every definition from point, line, plane and distance. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/distance-midpoint/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/distance-midpoint/Distance comes from the Pythagorean theorem; the midpoint averages the coordinates. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/angles-bisectors/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/angles-bisectors/Name and measure angles, and split them in half. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/basic-constructions/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/basic-constructions/Copy a segment and an angle, and bisect both. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/perpendicular-parallel-constructions/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/perpendicular-parallel-constructions/Construct a perpendicular bisector and a parallel through a point. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/inscribed-constructions/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/inscribed-constructions/Inscribe an equilateral triangle, a square and a regular hexagon. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/conditional-statements/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/conditional-statements/Write the converse, inverse and contrapositive, and find counterexamples. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/algebraic-proof/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/algebraic-proof/Justify each algebra step with a property. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/two-column-proofs/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/two-column-proofs/Chain given facts, definitions and theorems to reach a conclusion. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/line-angle-theorems/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/line-angle-theorems/Prove vertical angles are equal and that parallel lines give equal angles, and their converses. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/transformations-as-functions/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/transformations-as-functions/A transformation is a rule that sends each point to an image point. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/define-rigid-motions/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/define-rigid-motions/Define rotations, reflections and translations with angles, circles, perpendiculars and parallels. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/polygon-symmetry/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/polygon-symmetry/Find the rotations and reflections that carry a polygon onto itself. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/compose-transformations/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/compose-transformations/Apply a sequence of transformations and find one that maps a figure to another. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/congruence-rigid-motions/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/congruence-rigid-motions/Two figures are congruent when a rigid motion maps one onto the other. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/corresponding-parts/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/corresponding-parts/In △ABC ≅ △DEF, the letters tell which parts match. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/congruence-criteria/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/congruence-criteria/Three well-chosen parts are enough, and rigid motions show why. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/aas-hl/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/aas-hl/Two more shortcuts, including one for right triangles. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/congruence-proofs/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/congruence-proofs/Prove triangles congruent, then use matching parts. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/triangle-theorems/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/triangle-theorems/Prove the angle sum is 180° and the exterior angle theorem. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/isosceles-triangles/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/isosceles-triangles/Base angles of an isosceles triangle are equal, and the converse holds. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/bisectors-circumcenter/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/bisectors-circumcenter/Points on a perpendicular bisector are equally far from the endpoints. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/triangle-centers/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/triangle-centers/Angle bisectors, medians and altitudes each meet at one point. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/midsegments/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/midsegments/A midsegment is parallel to the third side and half as long. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/polygon-angle-sums/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/polygon-angle-sums/Split a polygon into triangles: (n − 2) × 180°. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/parallelogram-properties/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/parallelogram-properties/Opposite sides and angles are equal, and diagonals bisect each other. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/proving-parallelograms/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/proving-parallelograms/Use one of the tests, like two pairs of opposite sides equal. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/special-parallelograms/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/special-parallelograms/Equal diagonals mean a rectangle; perpendicular diagonals mean a rhombus. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/coordinate-proofs/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/coordinate-proofs/Use slope, distance and midpoint to prove facts about figures. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/dilation-properties/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/dilation-properties/A dilation keeps lines parallel and multiplies lengths by k. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/similarity-transformations/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/similarity-transformations/Two figures are similar if a dilation and rigid motions map one to the other. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/aa-similarity/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/aa-similarity/Two pairs of equal angles make triangles similar. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/sss-sas-similarity/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/sss-sas-similarity/Proportional sides, with or without an included angle, prove similarity. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/side-splitter/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/side-splitter/A line parallel to one side divides the other two sides proportionally. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/partition-segment/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/partition-segment/Find the point that splits a segment in the ratio a : b. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/similar-right-triangles/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/similar-right-triangles/The altitude to the hypotenuse makes three similar triangles. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/pythagorean-proof/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/pythagorean-proof/Use the three similar triangles to prove a² + b² = c². Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/special-right-triangles/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/special-right-triangles/Their sides are in fixed ratios: 1 : 1 : √2 and 1 : √3 : 2. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/trig-ratios/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/trig-ratios/Similar triangles make side ratios depend only on the angle. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/complementary-sine-cosine/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/complementary-sine-cosine/sin A = cos(90° − A). Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/solve-right-triangles/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/solve-right-triangles/Find missing sides with trig ratios and the Pythagorean theorem. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/inverse-trig-angles/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/inverse-trig-angles/Use sin⁻¹, cos⁻¹ and tan⁻¹ to find an angle from a ratio. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/elevation-depression/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/elevation-depression/Model heights and distances with right triangles. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/area-with-sine/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/area-with-sine/Area = ½ab sin C. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/law-of-sines/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/law-of-sines/Sides are proportional to the sines of their opposite angles. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/law-of-cosines/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/law-of-cosines/c² = a² + b² − 2ab cos C extends the Pythagorean theorem. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/circle-parts/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/circle-parts/Radius, diameter, chord, arc, tangent and secant. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/central-angles-arcs/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/central-angles-arcs/An arc's measure equals its central angle; all circles are similar. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/inscribed-angles/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/inscribed-angles/An inscribed angle is half its intercepted arc. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/tangent-lines/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/tangent-lines/A tangent is perpendicular to the radius at the point of contact. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/cyclic-quadrilaterals/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/cyclic-quadrilaterals/Opposite angles of an inscribed quadrilateral add to 180°. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/arc-length/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/arc-length/An arc is a fraction of the circumference: (θ/360) · 2πr. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/sector-area/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/sector-area/A sector is a fraction of the circle's area. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/circle-equation/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/circle-equation/(x − h)² + (y − k)² = r² comes from the distance formula. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/circle-completing-square/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/circle-completing-square/Rewrite x² + y² + Dx + Ey + F = 0 in center-radius form. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/parabola-focus-directrix/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/parabola-focus-directrix/A parabola is all points equally far from a point and a line. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/regular-polygon-area/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/regular-polygon-area/Area = ½ × apothem × perimeter. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/coordinate-area-perimeter/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/coordinate-area-perimeter/Use the distance formula to find perimeters and areas. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/cavalieri/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/cavalieri/Solids with equal cross-sections at every height have equal volume. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/pyramids-cones-spheres/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/pyramids-cones-spheres/Use V = ⅓Bh for pyramids and cones and V = (4/3)πr³ for spheres. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/surface-area-solids/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/surface-area-solids/Find surface areas of prisms, cylinders, pyramids, cones and spheres. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/cross-sections-revolution/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/cross-sections-revolution/Identify slices of solids and the solid made by spinning a shape. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/scaling-solids/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/scaling-solids/Scale lengths by k: areas scale by k², volumes by k³. Geometry · Math Ladderhttps://teddyrookbook.com/math/geometry/modeling-with-geometry/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/geometry/modeling-with-geometry/Model objects with shapes, use density, and solve design problems. Geometry · Math Ladder