November 2009
Beginner
368 pages
8h 55m
English
Content preview from Head First 2D Geometry
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spotting similar triangles
62 Chapter 2
You can spot similar triangles based on
just two angles
We know that angles in a triangle add up to 180 degrees, so once
you’ve got two angles in each triangle, you can always work out the
third.
And if you’ve noticed that two angles in one triangle are equal to two
angles in another triangle, then you can tell the triangles are similar
without even doing any math!
Look for two
equal angles
to spot similar
triangles.
You can tell these are the
same angle, even before you
work out what that angle is.
41
o
86
o
41
o
86
o
Circle the triangles below that you can be SURE are similar to the triangle repeated
in the design.
53
o
86
o
53
o
41
o
86
o
53
o
53
o
41
o
41
o
53
o
86
o
86
o
41
o
86
o
41
o
you are here 4 63
similarity and congruence
How many repeated angles are there in total on this diagram,
including the ones you’ve already marked plus the angles a
through i? (Count each value once—if it’s repeated don’t count it
again.)
Q:
What if the triangles are flipped, so one has a 41° on the
right and the other has a 41° angle on left? Are they similar?
A: As long as you can spot another angle which is in
both triangles then yes, they’re definitely similar. Similarity is
maintained even if your shape is reflected or rotated.
Q:
Isn’t using similarity kind of like cheating? Shouldn’t I
be working ...
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