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

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/
```
Associated Topics:
High School Geometry
High School Triangles and Other Polygons
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