Metric Relations in a Right Triangle, Theorems and Problems

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Geometry Problems 361 - 370

Ten Geometry Problems
Click the figure below to see problems 361-370 about Right triangle, Incircle, Incenter, Tangency points, Angle, Circle, Chord, Perpendicular, Congruence, Pythagoras, Obtuse, Diameter, Area, Circular sector.

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Level: High School, SAT Prep, College geometry

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

Geometry Problem
Click the figure below to see the complete problem 540 about Right Triangle, Square, Parallel, Perpendicular, Dissection, Area, Pythagoras.


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

Geometry Problem
Click the figure below to see the complete problem 539 about Right Triangle, Square, Parallel, Perpendicular, Dissection, Area, Pythagoras.


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Pythagoras Proofs, Uses, Facts, Interactive Mind Map

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Level: High School, SAT Prep, College geometry

Geometry Problems 101-110: Equilateral Triangle, Pythagoras, Median, Heron, Contact Triangle

Geometry Problem
Click the figure below to see problems 101-110 about Geometry Problems 101-110: Equilateral Triangle, Pythagoras, Median, Heron, Contact Triangle.


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Problems 101-110

Level: High School, SAT Prep, College geometry

Geometry Problems 91 - 100

Geometry Problem
Click the figure below to see problems 91-100 about Similarity, Triangles, Altitude, Parallel, Circumcircle, Parallelogram, Incenter, Area, Centroid, Quadrilateral, Archimedes, Pythagoras.


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Problems 91-100

Level: High School, SAT Prep, College geometry

Raphael's Fresco of the School of Athens - Video by Columbia University

Video and News
Masterpieces of Western Art at Columbia University has been a degree requirement for all College students and an integral part of the Core Curriculum since 1947.

For a 2D symmetry group, a kaleidoscopic point is a point of intersection of two or more lines of reflection symmetry.
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The School of Athens, Columbia University

The School of Athens by Raphael

Pythagoras, Euclid, Socrates, Plato, Aristotle and more together!
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The School of Athens

Problem 429: Circumscribed and Inscribed Regular Pentagon, Perpendicular, Measurement

Proposed Problem
Click the figure below to see the complete problem 429 about Circumscribed and Inscribed Regular Pentagon, Perpendicular, Measurement.


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Complete Problem 429

Level: High School, SAT Prep, College geometry

Problem 399: Right triangle, Midpoints, Distance, Pythagorean theorem, Congruence

Proposed Problem
Click the figure below to see the complete problem 399 about Right triangle, Midpoints, Distance, Pythagorean theorem, Congruence.


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Complete Problem 399
Level: High School, SAT Prep, College geometry

Problem 367. Square, Angle, 45 degrees, Pythagoras, Congruence, Similarity

Proposed Problem
Click the figure below to see the complete problem 367 about Square, Angle, 45 degrees, Pythagoras, Congruence, Similarity.


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Complete Geometry Problem 367
Level: High School, SAT Prep, College geometry

Problem 24: Right triangle, Altitude, Incircles

Proposed Problem



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gogeometry.com/problem/p024_right_triangle_incircles.htm

Level: High School, SAT Prep, College geometry

Albert Einstein and the Pythagorean theorem

A preteen Albert Einstein devised a new proof of the Pythagorean theorem

About the Pythagorean theorem, Albert Einstein wrote:

'For example I remember that an uncle told me the Pythagorean theorem before the holy geometry booklet had come into my hands. After much effort I succeeded in "proving" this theorem on the basis of the similarity of triangles ...



Read more at:
gogeometry.com/pythagoras/einstein_geometry_book.htm

Level: High School, SAT Prep, College geometry

Problem 265: Right Triangle, Pythagorean Theorem

Proposed Problem


See complete Problem 265 at:
gogeometry.com/problem/p265_pythagorean_theorem_right_triangle.htm

Level: High School, SAT Prep, College geometry

Problem 252. Rectangle, isosceles right triangle, square, areas

Proposed Problem


See complete Problem 252 at:
gogeometry.com/problem/p252_rectangle_triangle_square_area.htm

Level: High School, SAT Prep, College geometry

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Euclid's Elements Book II, Proposition 13: Law of Cosines

Acute Triangle


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gogeometry.com/geometry/euclid_elements_book_ii_proposition_13_cosines_law.htm

Level: High School, SAT Prep, College geometry

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Euclid's Elements Book II, Proposition 12: Law of Cosines.

Obtuse Triangle


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gogeometry.com/geometry/euclid_elements_book_ii_proposition_12_cosines_law.htm

Level: High School, SAT Prep, College geometry

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Elearn Geometry Problem 239: Square, Midpoints, Congruence, Pythagoras

Try to use elementary geometry (Euclid's Elements).




See complete Problem 239 at:
gogeometry.com/problem/p239_square_midpoints_congruence_pythagoras.htm

Level: High School, SAT Prep, College geometry

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Stewart Theorem

Visual illustration
A triangle and a cevian.



See complete illustration at:
www.gogeometry.com/pythagoras/stewart_theorem_triangle.htm

Level: High School, SAT Prep, College geometry