Types of Triangles

Date: 02/24/2003 at 16:16:18
From: Lisa
Subject: Types of Triangles

Dear Dr. Math,

What is the the difference between an isosceles and a scalene 
triangle? I always forget which is which!

Date: 02/25/2003 at 12:49:46
From: Doctor Hydrogen
Subject: Re: Types of Triangles

Hi Lisa,

Thanks for the question.

Equilateral triangles have three sides of equal length, and every 
angle is 60 degrees.

It is easy to remember the equilateral triangle as it has 'equil' in 
its name.

Isosceles triangles have two sides the same length and two angles
the same size.

Scalene triangles do not have any sides that are the same length, or 
any angles that are the same.

Isosceles and scalene triangles are more difficult to remember. It 
depends how your brain works. I used to remember it as 'SCAlene 
triangles are the least regular and most difficult and so are the most 
SCArey'. It worked for me, but if you can think of a better way, 
please let me know.

Does that help? If I can help any more with this problem or any 
other, please write back.

- Doctor Hydrogen, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 02/25/2003 at 13:12:26
From: Doctor Ian
Subject: Re: Types of Triangles

Hi Lisa,

To add to what Dr. Hydrogen said, a useful trick in trying to remember
names like these is to think about the pieces of words that they're
made from.  

'Lateral' always has to do with sides.  For example, the fins on the
side of a fish are 'lateral fins' (as opposed to the 'dorsal fins',
which are on the back).  Trade between two countries is 'bilateral
trade'.  In football, a 'lateral' is when the quarterback tosses the
ball to the side instead of throwing it forward, as in a regular pass.  
And so on. 

So 'equi-lateral' means 'equal sides', and in fact, all the sides of
an equilateral triangle are equal.  

The prefix 'iso' means 'same'.  For example, if you take chemistry,
you'll learn about 'isotopes', which are atoms that have the same
number of protons, and thus the same chemical behavior, but different
masses. (For example, you may have heard about using Carbon-14 to
figure out the ages of bones and artifacts found by archeologists. 
'Normal' carbon has 6 protons and 6 neutrons, for an atomic weight of
12. Carbon-14 has 6 protons and 8 neutrons, for an atomic weight of
14. Carbon-12 and Carbon-14 are called 'isotopes'.)  'Isometric'
exercise is exercise where the position of the muscles stays the same
(as when you press two hands together). Two things that have the same
shape are 'isomorphic'. And so on. 

An 'iso-sceles' triangle is one that has 'same legs' - as opposed to
'equal sides'. In an equilateral triangle, all the sides are the same; 
but in an isosceles triangle, two of the sides are 'legs', and the 
other is the 'base'.  And the legs are the same. 

'Scalene' comes from the Greek word for 'uneven', and a 'scalene'
triangle _is_ uneven: no side is the same length as any other. But to
be honest, usually I just remember that 'scalene' means 'not
equilateral or isosceles'.

So what can we learn from this? One lesson is that when you're having
trouble remembering a word, it's often a good idea to consult a
dictionary to find out the history of the word, because understanding
how a word was created can help it seem less arbitrary. Another
lesson is that many of the words that we find in math and science were
made up by people who were familiar with Latin and Greek, and so
studying either of those languages can make it much easier to learn
mathematical and scientific words!  

Hardly anyone studies them any more, but one of the things I'd go back
and change if I could, is that I'd want to study Latin as a child,
because the younger you are, the easier it is to learn new languages. 
I don't know if Latin is offered where you go to school, but if it is,
you'd be doing yourself a very big favor by taking it. 

I hope this helps!

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/