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Right Triangle Formulas | Lunes
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Pythagoras
and Right
Triangle Formulas-Facts. Level: High School, SAT
Prep, College |
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PYTHAGOREAN THEOREM, GEOMETRIC
MEAN, PRODUCT OF THE LEGS, ALTITUDE, PROJECTION: Proofs that use
similarity.
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SPECIAL RIGHT TRIANGLES:
Isosceles 45-45, 30-60, 37-53 (3-4-5)
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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.
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RIGHT TRIANGLE:
INRADIUS, EXRADII, SEMIPERIMETER (s), LEGS AND
HYPOTENUSE, AREA.
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RIGHT TRIANGLE: ORTHOGONAL
PROJECTIONS
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RIGHT TRIANGLE: ALTITUDE,
INRADII, INCENTER, AREAS.
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PYTHAGOREAN THEOREM: DIAGONAL OF A BOX
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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.
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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.
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THE PYTHAGOREAN CURIOSITY: Triangles and squares, fifteen conclusions.
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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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