Transcript Similar Triangles I

Similar Triangles I
Prepared by Title V Staff:
Daniel Judge, Instructor
Ken Saita, Program Specialist
East Los Angeles College
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© 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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AB
1.
=K
XY
BC
2.
=K
YZ
Scaling Factor
AC
3.
=K
XZ
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This can all be summarized as:
AB
=
XY
AC
BC
= K, Scaling factor
=
XZ
YZ
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Our problem becomes as follows:
12
8
10
=
=
= K, Scaling factor
6
4
5
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
AC
BC
=K
=
XZ
YZ
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AB
=
XY
BC
=
YZ
AC
=K
XZ
6
8
10
=
=
=K
4
6
8
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Do we have equality?
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!
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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
=

5
X
X=3
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
Y
So,
=2
4
Y =8
6
and
=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
AC
BC
=K
=
XZ
YZ
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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
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Our Website:
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