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Head First 2D Geometry by Dawn Griffiths, Stray

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similar triangles have the same angles
Similar triangles don’t just look the same
Similarity is a key piece of geometry jargon. If two shapes are similar, then
they don’t just look alike, one is an exact scaled version of the other. This
means that they have the same (equal) angles.
T
hese tr
iangles ar
e simil
ar. In
geometry terms, w
e don’t just
mean they kinda look the same.
Simil
ar triangles
don’t have t
o be
the same w
ay up.
86°
53°
41°
86°
53°
41°
41°
53°
86°
But don’t take our word for it…check that it all adds up:
Tick marks to show that
our line is parallel
86
o
41
o
53
o
41
o
53
o
86
o
1
Take a big triangle, and draw
Line part way up
the triangle
a line part way up the triangle,
parallel with the base.
2
This creates a mini triangle
which shares the angle at the
peak of the big triangle.
58 Chapter 2
similarity and congruence
Using what you know about parallel lines and the F pattern, find the two
mystery angles to complete the mini triangle you’ve created.
If the line is drawn parallel to one of the other sides, do you still end up with the
same angles in your mini triangle?
Remember the F
, N, Z pa
tterns
f
rom chapter 1? No? C
heck out
page 40.
?
?
86
o
41
o
53
o
?
?
41
o
86
o
53
o
41
o
86
o
53
o
?
?
you are here 4 59
the F pattern in action
Using what you know about parallel lines and the F pattern, find the two
mystery angles to complete the mini triangle you’ve created.
If the line is drawn parallel to one of the other sides, do you still end up with the
same angles in your mini triangle?
T
his F pa
ttern is
upside down and
back t
o f
ront!
The F pa
ttern
is upside down.
41
o
53
o
41
o
53
o
The angles always come out the same—it doesn’t matter which side the line is parallel to:
86
o
53
o
86
o
53
o
41
o
41
o
86
o
41
o
86
o
86
o
41
o
53
o
41
o
53
o
41
o
86
o
53
o
53
o
86
o
41
o
86
o
53
o
86
o
41
o
60 Chapter 2

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