# How to Master Right Triangle Math: From Pythagoras to 3-D Coordinates

Comprehensive coverage of right triangle formulas, including the Pythagorean theorem, catheti, hypotenuse, altitude, projection, inradius, circumradius, exradius, semiperimeter, area, special right triangles, Poncelet's theorem, general extension, and 2-D coordinates, as well as the Pythagorean theorem in 3-D.

 PYTHAGOREAN THEOREM, GEOMETRIC MEAN, PRODUCT OF THE CATHETUS, ALTITUDE, PROJECTION: Proofs that use similarity. SPECIAL RIGHT TRIANGLES: Isosceles 45-45, 30-60, 37-53 (3-4-5) CENTERS, INRADIUS, CIRCUMRADIUS, INCENTER, CIRCUMCENTER, ORTHOCENTER, CENTROID, PONCELET'S THEOREM, SAGITTA. Sagitta: The distance between the midpoint of an arc and the midpoint of its chord. RIGHT TRIANGLE: INRADIUS, EXRADII, SEMIPERIMETER (s), CATHETUS AND HYPOTENUSE, AREA. RIGHT TRIANGLE: ORTHOGONAL PROJECTIONS RIGHT TRIANGLE: ALTITUDE, INRADII, INCENTER, AREAS. PYTHAGOREAN THEOREM: DIAGONAL OF A BOX DISTANCE IN CARTESIAN COORDINATE: The Pythagorean Theorem provides an easy way to compute the straight line distance between any two points whose Cartesian coordinates are known. PYTHAGOREAN THEOREM IN THREE DIMENSIONS 3-D, De Gua's Theorem: In any tetrahedron with a cubic vertex O-ABC the square of the area of the face opposite the cubic vertex O-ABC is equal to the sum of the squares of the areas of the other three faces AOB, AOC, BOC. THE PYTHAGOREAN CURIOSITY: Triangles and squares, fifteen conclusions. THE GENERAL EXTENSION TO PYTHAGORAS' THEOREM: If any 3 similar shapes are drawn on the sides of a right triangle, then the area of the shape on the hypotenuse equals the sum of the areas on the other two sides.
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