Pythagoras and Right Triangles Theorems and Problems Index

Metric Relations in a Right Triangle, Theorems and Problems.

Pythagoras and Related Search Term Suggestions, Interactive Mind Map.

Right Triangles, Formulas and Facts
Pythagorean theorem, Similarity, Geometric mean, hypotenuse, cathetus, semiperimeter, altitude, median, similar shapes areas, centers, orthocenter, incenter, centroid, circumcenter, radius, inradius, circumradius, exradius, circles, incircle, circumcircle, excircle.

The General Extension to Pythagoras' Theorem.

The Pythagorean Curiosity Triangles and squares, fifteen conclusions.

Geometry Problem 668.
Right triangle, Incircles, Parallel, Common Tangent, Mind Map.

Geometry Problem 634
Right Triangle, Altitude, Incenters, Areas.

Geometry Problem 617
Right Triangle Area, Incircle, Incenter, Tangent, 90 Degrees.

Geometry Problem 608
Square with Right Triangles, Metric Relations, Congruence, Measurement.

Problem 572.
Right triangle, Median, Circle, Diameter, Excircle, Tangent circles.

Problem 570.
Square, Center, Right Triangles, Congruence, Collinearity.

Problem 567.
Right triangle, Incircle, Excircle, Collinear tangency points.

Problem 539.
Right Triangle, Square, Parallel, Perpendicular, Dissection, Area, Pythagoras.

Problem 540.
Right Triangle, Square, Parallel, Perpendicular, Dissection, Area, Pythagoras.

The significance of the Pythagorean theorem by Jacob Bronowski.
Pythagorean Theorem, 47th Proposition of Euclid's Book I.

Mind Map of the Pythagorean Theorem
Proofs by shears, translation, similarity. Facts.
 

Einstein and Pythagoras theorem proof
 

Pythagoras and Circle Area
 

Hippocrates and Squaring the Circle
 

Lunes of Hippocrates 1
 

Lunes of Hippocrates 2
 

Lunes of Hippocrates 3
 

Lunes of Hippocrates 4
 

Problem 544.
Right Triangle, Altitude, Median, Equal angles, Measure.

Problem 543.
Right Triangle, Altitude, Angle Bisector, Median.

Problem 542.
Right Triangle, Altitude, Angle Bisector, Perpendicular, 90 Degrees.

Problem 541.
Right Triangle, Altitude, Angle Bisector, Congruence.

Problem 534.
Right Triangle, Squares, Perpendicular, Dissection, Areas.

Problem 522.
Right Triangle, Circle, Diameter, Tangent.

Classical Theorems.

Proposed Problem 437.
Tangent Circles, Diameter, Chord, Perpendicular, Congruence, Measurement.

Proposed Problem 436.
Tangent Circles, Diameter, Chord, Perpendicular, Congruence, Measurement.

Proposed Problem 430.
Circumscribed and Inscribed Regular Pentagon, Perpendicular, Areas.

Proposed Problem 429.
Circumscribed and Inscribed Regular Pentagon, Perpendicular, Measurement.
Pythagoras

Proposed Problem 363.
Right triangle, Congruence, Angles.

Proposed Problem 317.
Right triangle and Inscribed Squares.

Proposed Problem 303.
Triangle, Angle bisector of 90 degrees.

Proposed Problem 294.
Right triangle, Circumcenter, Excenter, Hypotenuse, Perpendicular.

Proposed Problem 275.
Right Triangle, Circumcircle, Sagitta, Inradius.

Proposed Problem 239. Square, Midpoints, Lines, Congruence, Pythagoras.

Proposed Problem 220. Right Triangle, Altitude, Angle Bisector, Distance, Arithmetic Mean.

Proposed Problem 207. Right Triangle, Hypotenuse, Inradius, Exradius relative to the hypotenuse.

Proposed Problem 206. Area of a Right Triangle, Inradius, and Exradius relative to the hypotenuse.

Proposed Problem 205. Right Triangle Area, Exradii relatives to legs or catheti.

Proposed Problem 204. Right Triangle, Incircle, Excircles, Inradius, Exradii.

Proposed Problem 203. Right Triangle, Excircles, Exradii, Hypotenuse.

Proposed Problem 202. Right Triangle, Incirle, Excircles relatives to catheti, Points of Tangency, Exradius, Semiperimeter.

Proposed Problem 201. Right Triangle, Excircles, Points of Tangency, Exradius, Semiperimeter.

Proposed Problem 200. RightTriangle, Incircle, Excircles, Points of Tangency, Inradius.

Proposed Problem 187. Right Triangle, Altitude, Incenters, Circles, Angles.

Proposed Problem 186. Right Triangle, Altitude, Incenters, Circles.

Proposed Problem 183. Right Triangle, Hypotenuse Trisection Points, Squares of the Distances.

Proposed Problem 102.Equilateral Triangle Area, Interior Point.

Proposed Problem 101.Equilateral Triangle, Pythagorean Theorem, Angles.

Proposed Problem 99: Circle Area, General Extension to Pythagoras' Theorem.

Proposed Problem 76: Area of a Circle. Square, Circle, Circular Sector. 

Proposed Problem 218. Right triangle, Altitude and Projections.

Proposed Problem 217. Right triangle, Altitude and Projections.

Proposed Problem 49. Angles and right triangle.

Sangaku Problem 41. "Mickey Mouse" shape: Three circles representing head and ears.

Triangle and Squares 19  

Proposed Problem 38.
Right Triangle, altitude, incircles, incenters, and angles.

Proposed Problem 37.
Right Triangle, altitude, incircles, incenters, and orthocenter.

Problem 36.
Right Triangle, altitude, incircles and inradii.

Proposed Problem 34.
Right triangle, cevian, incircles, tangents and inradius.

Archimedes' Book of Lemmas
 

Euler and his beautiful and extraordinary formula

Problem 31. Right Triangle, Incircle, Collinears.
Problem 30. Right Triangle, Incircle, Inradius.

Proposed Problem 29.
Right Triangle, altitude, incircle and inradius. Ten conclusions.

Problem 29: Geometry Help.
Facts you should know.

Proposed Problem 28
Right Triangle, altitude, incircles and inradius.

Proposed Problem 27
Right Triangle, incircles and inradius.

Proposed Problem 26
Right Triangle, altitude, incircles and inradius.

Proposed Problem 25
Right Triangle, altitude, incircles and inradius.

Proposed Problem 24
Right Triangle, altitude, incircles and inradii.

Proposed Problem 23
Right Triangle, altitude, incircles and inradii.

Proposed Problem 22
Right Triangle, altitudes, incircles and inradii.

Proposed problem 20
Right Triangle, incircles and inradii.

Proposed problem 19
Right Triangle and Excenter

Poncelet Theorem

Sangaku Problem 3

• Geometry

• Formulas: Pythagorean theorem, Geometric mean, Product of the catheti (legs), altitude, Projection

• Special Right Triangles

• Centers, Inradius, Circumradius, Incenter, Circumcenter, Orthocenter, Centroid, Poncelet, Sagitta

• Inradius, Exradii, Semiperimeter, Area

• Orthogonal Projections

• Altitude, Inradii, Incenter, Areas

• Pythagorean Theorem: Diagonal of a Box

• Distance in Cartesian Coordinate

• De Gua's Theorem

• The General Extension to Pythagoras' Theorem

• The Pythagorean Curiosity

• Einstein and Pythagoras theorem proof

• Squaring the circle? Lunes 1, 2, 3, 4, 5

• Mind Map of the Pythagorean Theorem

• Problems: 19, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 34, 36, 37, 38, 41, 49, 58

• Video: Right Triangle and Pythagoras

• The significance of the Pythagorean theorem  by Jacob Bronowski.