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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
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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