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 Triangle and Squares. Level: High School, SAT Prep, College geometry

Welcome to Triangle and Squares! . Site created and maintained by Antonio Gutierrez.

The following visual illustrations show the result of exploring triangle and squares with dynamic geometry software.

Some of the results under Triangles and Squares are special cases of Van Aubel's theorem which relates to squares on the sides of a quadrilateral. When two vertices of the quadrilateral coincide some of the special cases here are obtained. For generalizations of Van Aubel's theorem (and associated generalizations for triangles when two vertices coincide) go to:

Dual Generalizations of Van Aubel's Theorem by Michael de Villiers and
Generalizing Van Aubel: Michael de Villiers' Theorems. Illustration.

 

Triangle & Squares: Table of Content

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30.

Pythagoras curiosity. Online tutoring.

The Pythagorean Curiosity Triangles and squares, fifteen conclusions

29.

Triangle Square Theorem 1. Elearning, Online Tutoring

Triangle and Squares Theorem 1: with Interactive Geometry Software
Step-by-Step construction, Manipulation, and animation.

28.

Bottema Theorem. Elearning.

Bottema's Theorem: Triangle and Squares with Interactive Geometry Software
Step-by-Step construction, Manipulation, and animation.

27.

Proposed Problem 70: Squares inscribed in a triangle, Similarity.

 

26.

Proposed Problem 69: Square inscribed in a triangle, Similarity.

 

25.

Hinged tessellation, Dynamic geometry

Interactive Hinged tessellation. Square tessellation - Dynamic Geometry.
Please be patient while the applet loads on your computer. This Java applet requires Java 1.3 or higher.

24.

Generalizing Van Aubel: Michael de Villiers' Theorems.
Triangle and Squares in the News 

23.

Van Aubel

Van Aubel's Theorem. Quadrilateral with Squares. Proof with animation.
 

22.

Triangle and Squares 22
 

21.

Triangle and Squares 21
See also: Triangle and Squares 19

20.

Triangle and Squares 20

19.

Triangle and Squares 19  

18.

Triangle and Squares 18  Sangaku Problem

17.

Triangle and Squares 17

16.

Triangle and Squares 16

15.

Triangle and Squares 15

14.

Triangle and Squares 14

13.

Triangle and Squares 13

12.

Triangle and Squares 12

11.

Triangle and Squares 11

10.

Triangle and Squares 10

9.

Triangle and Squares 9

8.

Triangle and Squares 8

7.

Triangle and Squares 7

6.

Triangle and Squares 6

5.

Triangle and Squares 5

4.

Triangle and Squares 4

3.

Triangle and Squares 3

2.

Triangle and Squares 2

1.

Triangle and Squares 1

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Last updated: May 1, 2008