

How to Master Right Triangle Math: From Pythagoras to 3D 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 2D coordinates, as well as the Pythagorean theorem in 3D.

PYTHAGOREAN THEOREM, GEOMETRIC
MEAN, PRODUCT OF THE CATHETUS, ALTITUDE, PROJECTION:
Proofs that use
similarity.

SPECIAL RIGHT TRIANGLES:
Isosceles 4545, 3060, 3753 (345)

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 3D, De Gua's
Theorem: In any
tetrahedron with a cubic vertex OABC the square
of the area of the face opposite the cubic vertex OABC 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.







