T

hey’re not congruent

because even though they ar

e

simil

ar, one is sma

ller than

the other.

T

hese thr

ee arrows

ar

e congruent.

T

hese thr

ee

arrows ar

e

congruent.

Congruent

Tw

o s

hap

es are congruent

if they’re simil

ar and a

lso

the same size.

Tw

o s

hap

es are incongruent

if they ar

e not the same

size.

similarity and congruence

Similar shapes that are the same size are congruent

Shapes that are similar have equal angles and are proportional, but if

they’re actually the exact same size, then we say that they’re congruent.

T

he big arrows and

the sma

ll arrows are

SIMILA

R but not

CONGRU

E

NT

.

How can spotting congruence save you even more time and work

than similarity?

you are here 4 81

make your problem smaller

But calculating the

corner angles of squares and

equilateral triangles is the easy

part! How’s congruence going

to help with all those angles

between the arrows? Huh?

For starters, congruence means you

only have to do one third of the work.

Those overlap angles are much trickier, but you’ll only

have to find each one once—then you can just copy it

to each of the angles congruent with it.

Original

Problem

Smaller

Problem

Similarity &

Congruence

Look how much of

the problem just

vanished!

82 Chapter 2

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