Congruent Triangles - SSS Test

Date: 11/16/98 at 10:38:07
From: Doug
Subject: SSS Geometry

Can you explain SSS to me?

Date: 11/16/98 at 11:04:37
From: Doctor Santu
Subject: Re: SSS Geometry

Yes, Doug!

Suppose you have two different triangles, ABC and PQR. The question is: 
are they exactly the same size and shape? That's what we mean by 
"congruent."

A triangle has 6 parts: 3 sides, and 3 angles. If two triangles are 
congruent, all six parts of one triangle will match all six 
corresponding parts of the other.

There are tests we can do to check whether two triangles are congruent, 
and one of them is the SSS test. If three sides of one triangle are the 
same lengths as three sides of the other triangle, then they have to be 
congruent. (This is useful, because you only need to check three 
things, and you know that the other three parts will match up 
automatically. The name of the test, SSS, stands for "side-side-side".  
There's another one called the SAS test, for Side-Angle-Side.)

Suppose in triangle ABC,  AB = 12, BC = 15, and AC = 9.
Suppose in triangle PQR,  PQ = 9, QR = 15, and PR = 12.

What would you say: are they congruent according to the SSS test?

Yes, they are. Even though the order is different, the sides do match 
up, so we say that ABC is congruent to PRQ. (You have to name them so 
that corresponding angles match up. I'm not sure whether your teacher 
is picky about the difference between triangle PQR and triangle PRQ; 
I am!)

Sometimes triangles are NOT congruent; for example, if one triangle has 
sides 2, 3 and 4, and the other triangle has sides 3, 4, 4, they're not 
congruent. Two sides match up, but the other side doesn't.

Write back if you need a more detailed answer.

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