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### A Triangle with Three Right Angles

```
Date: 12/01/1999 at 08:48:06
From: Jimmy Stine
Subject: Geometry

For extra credit my teacher assigned this problem: How could you make
a triangle with three right angles? I have tried for a while to do it
and I have to somehow make a model of a triangle with 3 right angles.
Could you please send me the solution?
```

```
Date: 12/01/1999 at 12:13:27
From: Doctor Peterson
Subject: Re: Geometry

Hi, Jimmy.

This is impossible for a real triangle on a plane, since, as you
probably know, the sum of angles must be 180 degrees. But it is
possible in spherical geometry, where we use the word "line" to mean a
great circle (a circle around the sphere whose plane goes through the
center of the earth).

Imagine starting, say, at the North Pole, walking some distance in a
"straight line," turning left 90 degrees, walking some distance, then
turning left 90 degrees again, and getting back where you started. Can
you find a way to do this, and end up 90 degrees from your original
direction?

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Euclidean/Plane Geometry
High School Geometry
High School Non-Euclidean Geometry
High School Triangles and Other Polygons
Middle School Geometry
Middle School Triangles and Other Polygons
Middle School Two-Dimensional Geometry

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