November 2009
Beginner
368 pages
8h 55m
English
Content preview from Head First 2D Geometry
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you are here 4 81
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.
The big arrows and
the small arrows are
SIMILAR but not
CONGRUENT.
They’re not congruent
because even though they are
similar, one is smaller than
the other.
These three arrows
are congruent.
These three
arrows are
congruent.
How can spotting congruence save you even more time and work
than similarity?
Congruent
Two shapes are congruent
if they’re similar and also
the same size.
Two shapes are incongruent
if they are not the same
size.
82 Chapter 2
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!
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