Idiot\'s Guides Basic Math and Pre-Algebra

234 Part 3: The Shape of the World

Similarity and Congruence ................................................................................................

When we talk about how polygons relate to one another, we most often talk about congruence

and similarity. Two polygons are congruent if they are the same shape and the same size. They’re

copies of one another, as if you ran one through a copier. Two polygons are similar if they’re

the same shape but different sizes. Think about enlarging a photo without distorting the image.

Polygons of any number of sides can be congruent or similar, but most often you will encounter

congruent triangles or similar triangles.

Congruent Triangles

Triangles are congruent if they are the same shape and the same size. Because the size of the

angles controls the shape of the triangle, in a pair of congruent triangles, you can match up angles

that are the same size. In other words, corresponding angles are congruent. Because the length of

sides controls size, corresponding sides are of equal length, or congruent.

Two triangles are congruent if each pair of corresponding sides are congruent and

each pair of corresponding angles are congruent.

If nARM nLEG, ’A and ’L will be the same size, ’R will have the same measurement as

’E, and m’M = m’G. Sides are congruent as well. ARLE, RM EG and AMLG.

The order in which the vertices of the triangle are named tells you what matches. You can

sometimes tell what matches by looking at a picture, but unless you’re told the measurements,

or you can actually measure, you can’t always be certain. The order in which the vertices of the

triangles are named will tell the correct match-up.

E

L

G

M

A R