Similar Triangles I Prepared by Title V Staff: Daniel Judge, Instructor Ken Saita, Program Specialist East Los Angeles College EXIT BACK NEXT © 2002 East Los Angeles College. All rights reserved. Click one of the buttons below or press the enter key
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Similar Triangles I
Prepared by Title V Staff:
Daniel Judge, Instructor
Ken Saita, Program Specialist
East Los Angeles College
EXIT BACK NEXT © 2002 East Los Angeles College. All rights reserved.
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In geometry, two polygons are similar
when one is a replica (scale model) of
the other.
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Consider Dr. Evil and Mini Me from
Mike Meyers’ hit movie Austin Powers.
Mini Me is supposed to be an exact
replica of Dr. Evil.
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Triangles are a class of polygons in
geometry. Therefore we can talk about
triangles that are similar. The following
is a picture of similar triangles.
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Note: One triangle is a scale model of the
other triangle.
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Q: How do we truly know that the
above two triangles are similar (scaled
model)?
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Answer– We must take a closer look at
the sides of our triangles. The
following conditions must all be
satisfied.
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1.
2.
3.
AB=K
XY
BC=K
YZ
AC=K
XZ
Scaling Factor
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This can all be summarized as:
AB =
XY
BC =
YZ
AC = K,
XZScaling factor
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Our problem becomes as follows:
12 8 10 = = = K,
6 4 5Scaling factor
This tells us that ABC and XYZ are
similar.
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Q: Can these triangles be similar?
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Answer—Yes, right triangles can also
be similar but use the criteria.
AB =
XY
BC =
YZ
AC = K
XZ
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6 8 10 = = = K
4 6 8
AB =
XY
BC =
YZ
AC = K
XZ
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6 8 10 = = = K
4 6 8
6 8 = 1.5 but = 1.3
4 6
This tells us our triangles are not
similar. You can’t have two different
scaling factors!
Do we have equality?
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Q: The two triangles below are known
to be similar, determine the missing
value X.
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Answer– Using the fact that our
triangles are similar . . .
7.5 4.5 = X = 3
5 X
The missing side has a length that’s 3
units. The picture should look like
this . . .
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Q: The following triangles are similar.
Can you determine the missing sides X
and Y?
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Answer– Using the criteria,
10 Y 6 10 = = , but = 2 !
5 4 X 5
YSo, = 2
4
Y = 8
6and = 2
X
X = 3
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Our triangles should look like this:
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Let’s take a closer look at the criteria
that tells us when triangles are similar:
AB =
XY
BC =
YZ
AC = K
XZEXIT BACK NEXT
Mathematicians find this next
relationship useful as well.
AB XY AB XY AC XZ = , = , =
BC YZ AC XZ BC YZ
Why?
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End of Similar Triangles I
Title V
East Los Angeles College
1301 Avenida Cesar Chavez
Monterey Park, CA 91754
Phone: (323) 265-8784
Email Us At:
Our Website:
http://www.matematicamente.org
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