Pythagoras and Right Triangle Formulas-Facts.
Level: High School, SAT Prep, College

Geometry, Machu Picchu

PYTHAGOREAN THEOREM, GEOMETRIC MEAN, PRODUCT OF THE LEGS, 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), LEGS 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 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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