Pythagoras and Right Triangles and Problems

Plane Geometry: Pythagoras, Right Triangle, Metric Relations Index 1

Pythagoras' truth,
Right triangle's sacred gift,
Sides in harmony.
Square of hypotenuse sings,
Geometry's masterpiece.


Metric Relations in a Right Triangle

Metric Relations in a Right Triangle, Theorems and Problems.

Einstein and Pythagoras theorem proof
Discovering the Mathematical Mind of Albert Einstein: The Fascination with Geometry and the Pythagorean Theorem

Pythagorean spiral or Square Root Spiral or Spiral of Theodorus

Pythagorean spiral or Square Root Spiral or Spiral of Theodorus.

Pythagoras and Delaunay Triangulation Art, iPad Apps: Poly

Pythagoras and Delaunay Triangulation Art, iPad Apps: Poly.
Polygonal Art Illustration.

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.

Geometry Problem 1563

Geometry Problem 1563: Perpendicularity in a Right Triangle involving the Altitude, Angle bisectors, and Midpoints.

Geometry Problem 1562

Geometry Problem 1562: Proof of Collinearity in a Right-angled Triangle involving the Altitude, Angle bisectors, and Midpoint.

Geometry Problem 1557

Geometry Problem 1557: Calculate the Angle DHG in Right Triangle ABC. The problem involves: equilateral, isosceles, midpoint and congruence

Geometry Problem 1556

Geometry Problem 1556: Right Triangle ABC and Inscribed Circle. The problem involves circle, chords, tangent, perpendicular lines, and congruence

Geometry Problem 1554

Geometry Problem 1554: Finding the Length of Side AB in Triangle ABC

Geometry Problem 1550

Geometry Problem 1550: Solving for Segment BD: An Angle Puzzle in Right Triangle ABC: A High School Level Investigation

Geometry Problem 1548

Geometry Problem 1548: Exploring Segment DE Length in Triangle ABC with a 45-Degree Angle and Intersecting Altitudes

Geometry Problem 1547

Geometry Problem 1547: Tangents' Dance: Exploring B-to-AC Distance in a Circle's Grasp

Geometry Problem 1543

Geometry Problem 1543: Calculating the Area of Quadrilateral ABED in a Square with a Side Length of 20 and an Intersecting Arc.

Geometry Problem 1542

Geometry Problem 1542: Unraveling a Geometric Puzzle with a Circumscribed Right Triangle and Square to the Same Circle for School and College.

Geometry Problem 1539

Geometry Problem 1539 Demystified: Unraveling the Lengths in an Isosceles Triangle with Altitude and Tangent Secrets!.

Geometry Problem 1533

Geometry Problem 1533: Discovering Relationships between Angles and Lines in an Exterior Right Triangle of a Square - A High School Challenge.

Geometry Problem 1532

Geometry Problem 1532: Crack the Code of Geometry Problem 1532: How to Find the Angle in a Square with a Tangent Semicircle! - A High School Challenge.

Geometry Problem 1531

Geometry Problem 1531: Discover How to Calculate the Length of a Chord in a Circle with Diameter Intersection and an Angle between the Diameter and Chord - A High School Challenge.

Geometry Problem 1525

Geometry Problem 1525 and a Thematic Poem.
Unveiling the Secrets of an Equilateral Triangle in Right Triangle Geometry: Finding the Midpoint Distance between Segments.

Geometry Problem 1509

Geometry Problem 1509 and Poem.
Congruence of Triangles in a Trapezoid and a Square, Measurement. Difficulty Level: High School.

Geometry Problem 1502

Geometry Problem 1502.
Right Triangle, Incircle, Inradius, Geometric Mean of 2 Inradii, Angle Bisector, Perpendicular, Tangential Quadrilateral.

Geometry Problem 1492

Geometry Problem 1492.
Right Triangle, Altitude, Incenters, Angle, Measurement.

Geometry Problem 1489

Geometry Problem 1489.
Right Triangle, Angle Bisectors, Perpendicular, Measurement.

Geometry Problem 1488

Geometry Problem 1488.
Right Triangle, Altitude, Incircle, Tangent, Measurement.

Geometry Problem 1487

Geometry Problem 1487.
Right Triangle, Altitude, Incircle, Tangent, Measurement.

Geometry Problem 1486

Geometry Problem 1486.
Right Triangle, Altitude, Incircle, Tangent, Measurement.

Geometry Problem 1484

Geometry Problem 1484.
Right Triangle, Altitude, Incircles, Inradius, Measurement.

Dynamic Geometry 1483

Geometry Problem 1483.
Isosceles Right Triangle, Excenter, Perpendicular, Measurement.

Dynamic Geometry 1482

Geometry Problem 1482.
Right Triangle, Perpendicular, Double Angle, Measurement.

Problem 1439

Geometry Problem 1439.
Rectangle, Diagonal, Perpendicular, Circles, Areas, Art, Poster, Typography, iPad Apps.

Problem 1436

Geometry Problem 1436.
Right Triangle, Altitude, Excircles, Excenters, Geometric Mean, Measurement, Art, Poster, Typography, iPad Apps.

Problem 1390

Geometry Problem 1390.
Triangle, any point, perpendicular, sum of the squares.

Problem 1386 Thabit ibn Qurra Theorem,Pythagorean Theorem to any triangle

Geometry Problem 1386.
Thabit ibn Qurra (826 -901) Theorem and more conclusions, generalized Pythagorean Theorem to any triangle.

Pythagoras curiosity. Online tutoring.

Geometry Problem 884: The Pythagorean Curiosity
Right Triangles and squares, fifteen conclusions.

iPad Geoboard: Pythagorean Theorem proof by Leonardo 

Geoboard for iPad Pythagorean Theorem Proof by Leonardo.

Right Triangle, Altitude, Incircle Index

Right triangle, Altitude, Incircle
Right Triangle, Altitude to the Hypotenuse, Incircle, Incenter, Inradius, Angle Bisector, Theorems and Problems, Index.

Right Triangle Word Cloud

Right Triangle Word Cloud. Geometry for Kids.

Geometry problem 1255

Geometry Problem 1255.
Right Triangle, Angle, 90 Degrees, Perpendicular, Collinear Points.

Geometry problem 1253

Geometry Problem 1253.
Triangle, Orthocenter, Circle, Circumcircle, Altitude, Perpendicular, 90 Degree, Concurrency.

Geometry problem 1211

Geometry Problem 1211
Right Triangle, Altitude, Angle Bisector, 45 Degrees.

Geometry problem 1203

Geometry Problem 1203
Right Triangle, Square, Angle Bisector, Three Congruent Quadrilaterals.

Geometry problem 1200

Geometry Problem 1200
Square, Right Triangle, Perpendicular, 90 Degrees, Equal Areas.

Geometry problem 1198

Geometry Problem 1198
Right Triangle, Square, Rectangle, Quadrilateral, Altitude, Equal Areas.

Geometry problem 1196

Geometry Problem 1196
Parallelogram, Midpoint, Metric Relations.

Geometry problem 1195

Geometry Problem 1195
Square, Two Rectangles, Congruence, Metric Relations.

Geometry problem 1194

Geometry Problem 1194
Equilateral Triangle, Perpendicular, Distance, Side, Metric Relations.

Geometry problem 1165

Geometry Problem 1165.
Right Triangle, Circle, Center, Radius, Cathetus, Perpendicular, 90 Degrees, Perimeter, Metric Relations.

Geometry problem 1159

Geometry Problem 1159.
Triangle, Circumcircle, Sagitta, Chord, Arc, Metric Relations.

Geometry problem 1158

Geometry Problem 1158.
Four Tangent Circles, Tangent Chord, Radius, Metric Relations.

Geometry problem 1157

Geometry Problem 1157.
Four Circles, Mutually Tangent, 90 Degrees, Radius, Metric Relations.

Geometry problem 1156

Geometry Problem 1156.
Square, Tangent Line, 90 Degrees, Metric Relations.

Geometry problem 1155

Geometry Problem 1155.
Right Triangle, Altitude, Incenter, Incircle, Area.

Geometry problem 1154

Geometry Problem 1154.
Sangaku: Three circles and a tangent line.

Geometry problem 1151

Geometry Problem 1151.
Circle, Diameter, Chord, Perpendicular, 90 Degrees, Metric Relations.

Geometry problem 1148

Dynamic Geometry Problem 1148
Static Geometry Problem 1148.
Right Triangle, Incircle, Circumcircle, Tangent, Radius. GeoGebra, HTML5 Animation for Tablets (iPad, Nexus).

Geometry problem 1128

Geometry Problem 1128.
Right Triangles, Medians, Parallel, Angles, Congruence, Half the measure.

Geometry Problem 1120

Geometry Problem 1120.
Isosceles Right Triangle, 120 Degree, Angle, Equilateral, Metric Relations.

Geometry Problem 1118

Geometry Problem 1118.
Right Triangle, Angle Trisection, Concyclic Points, Cyclic Quadrilateral.

Geometry Problem 1117

Geometry Problem 1117.
Right Triangle, Angle Trisection, 90 Degrees, Parallel Lines.

Geometry Problem 1116

Geometry Problem 1116.
Right Triangle, Angle Trisection, 90 Degrees, Perpendicular Lines.

Geometry Problem 1115

Geometry Problem 1115.
Right Triangle, Angle Trisection, Equilateral Triangle.

Geometry Problem 1114

Geometry Problem 1114.
Right Triangle, Angle Trisection, Isosceles, Congruence.

Geometry Problem 1111

Geometry Problem 1111.
Right Triangle, External Squares, Cathetus, Angle Bisector, Area, Geometric Mean.

iPad Geoboard: Pythagorean Theorem proof 

Geoboard for iPad Pythagorean Theorem Proof, Squares (Problem 540).

Pythagoras Theorem, 47th Proposition of Euclid's Book I

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.

Word Cloud of Pythagoras

Word Cloud of Pythagorean Theorem

Pythagoras and Circle Area

Hippocrates and Squaring the Circle

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Last updated: Jul 16, 2024