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### Dissecting a Square into Acute Triangles

```
Date: 11/09/1999 at 11:26:31
Subject: Geometry

Can you dissect a square into a finite number (fewer than 14) of acute
triangles?
```

```
Date: 11/09/1999 at 13:07:06
From: Doctor Rob
Subject: Re: Geometry

Put the vertices of the square at A(0,0), B(10,0), C(10,10), and
D(0,10). Mark points along the sides at E(5,0), F(10,6), G(5,10), and
H(0,6). Mark points in the interior at I(3,4), J(7,4), K(6,7), and
L(4,7). Then connect AI, BJ, CK, DL, EI, EJ, FJ, FK, GKJ, GLI, HI, and
HL. Prove that GKJ and GLI are straight lines. Then prove that the 12
triangles formed are all acute.

For just 8 triangles, see the top of David Eppstein's page from the
Geometry Junkyard, Triangles and Simplices:

http://www1.ics.uci.edu/~eppstein/junkyard/triangulation.html

- Doctors Rob and Schwa, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Geometry
High School Triangles and Other Polygons
Middle School Geometry
Middle School Triangles and Other Polygons

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