Download Similar Triangles I

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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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The following are similar figures.
I
II
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The following are non-similar figures.
I
II
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Feefee the mother cat, lost her daughters, would you
please help her to find her daughters. Her daughters have
the similar footprint with their mother.
Feefee’s
footprint
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1.
Which of the following is similar to the
above triangle?
A
B
C
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Note: One triangle is a scale model of the
other triangle.
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How do we know if two
triangles are similar or
proportional?
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Triangles are similar (~)
if corresponding angles
are equal and the ratios
of the lengths of
corresponding sides are
equal.
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Interior Angles of Triangles
B
A
C
The sum of the measure
of the angles of a
triangle is 1800.
C =1800
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Determine whether the pair of triangles is similar.
Justify your answer.
Answer: Since the corresponding angles have equal
measures, the triangles are similar.
If the product of the
extremes equals the
product of the means
then a proportion
exists.
a c
=
b d
bc = ad
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This tells us that  ABC and  XYZ are
similar and proportional.
AB
=K
XY
BC
=K
YZ
12
=2
6
8
=2
4
AC
=K
XZ
10
=2
5
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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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If we are given that two
triangles are similar or
proportional what can we
determine about the
triangles?
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The two triangles below are known to
be similar, determine the missing value
X.
7.5 4.5
=
5
x
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7.5 4.5
=
5
x
54.5 = 7.5x
22.5 = 7.5x
3= x
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In the figure, the two triangles are similar.
What are c and d ?
A
5
P
10
c
B
R
4
d
Q
6
10 c
=
5 4
C
40 = 5c
8=c
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In the figure, the two triangles are similar.
What are c and d ?
A
5
P
10
c
B
R
4
d
Q
6
C
10 6
=
30 = 10d
5 d
3=d
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Sometimes we need to measure a distance
indirectly. A common method of indirect
measurement is the use of similar triangles.
17 6
=
102 h
36 = h
h
6
17
102
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