Associated Topics || Dr. Math Home || Search Dr. Math

### Right Angles in a Triangle

```
Date: 3/8/96 at 13:36:1
From: Anonymous
Subject: right angles

How many right angles (90 degrees) can a triangle have?
```

```
Date: 3/17/96 at 19:42:53
From: Doctor Jodi
Subject: right angles

That depends where the triangle is...

If it's on a plane (like a table top), only one.

If it's on a sphere, it could have more than one.  Can you picture
this?

The straight lines in a plane - the shortest distance between any two
points - are analogous to great circles on a sphere.

The general word for the shortest path between two points in any
surface is a <b>geodesic</b>.  Straight lines in the plane and great
circles on the sphere are both sorts of geodesics.

What, you may ask, does a great circle look like?

Well, suppose you take a play-dough sphere and cut it into two equal
parts (two semi-spheres).  The line you cut on is a <b>great circle</b>.

There are infinitely many great circles on the sphere; you could
make infinitely many semi-spheres, if you felt like it.

Now, if instead of cutting your play-dough sphere, you just MARK
several great circles on it, you can make a triangle.  (Triangles on
any surface are made with geodesics, so on a sphere, you need to use
great circles).

How many perpendicular great circles can you use in one triangle?
That's how many right angles it will have...

Good luck!

-Doctor Jodi,  The Math Forum

```
Associated Topics:
Middle School Geometry
Middle School Triangles and Other Polygons

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.
http://mathforum.org/dr.math/