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, 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. 

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 1578:
Find the Area of a Bicentric Quadrilateral with Perpendicular Extensions of Opposite Sides!. 

Geometry Problem 1572:
Calculate Angle C with Geometric Methods Using Sides AB=17, BC=25, and Angle A=45 Degrees 

Geometry Problem 1571:
Prove that the intermediate angle in a Pythagorean Triple 72425 measures 74 degrees. 

Geometry Problem 1569:
Prove a Relationship: EG Equals the Incircle Diameter in Triangle ABC with Square CDEF. 

Geometry Problem 1564:
Find the Area of Quadrilateral BGDJ in a Right Triangle involving the Altitude, Angle bisectors, and Midpoints. 

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

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

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

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

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

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

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

Geometry Problem 1547: Tangents' Dance: Exploring BtoAC Distance in a
Circle's Grasp 

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Geoboard
for iPad Pythagorean Theorem Proof by Leonardo. 

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

Right Triangle Word Cloud.
Geometry for Kids. 

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

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

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

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

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

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

Geometry Problem 1196
Parallelogram, Midpoint, Metric Relations. 

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 Pythagorean Theorem


Pythagoras
and Circle Area


Hippocrates and
Squaring the Circle

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Last updated: Aug 17, 2024

