11.5 Similar Triangles

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11.5 Similar Triangles

• Identifying Corresponding Sides of Similar
  Triangles

By Shaunta Gibson
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Similar Triangles are triangles that have the
same shape but not necessarily the same size.
B
E
D
F
C
A
In the diagram above, triangle ABC is equal to
triangle DEF. We write it as ABC DEF. In the
diagram, each angle of ABC corresponds to an
angle of DEF as follows
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Similar Triangles are triangles that have the
same shape but not necessarily the same size.
B
E
C
F
A
D
angle A angle D angle B angle E
angle C angle F Also, each
side of ABC corresponds to a side of DEF AB
corresponds to DE BC corresponds to EF AC
corresponds to DF
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In similar triangles, corresponding sides are the
sides opposite the equal angles.

• When we write that two angles are similar, we
  name them so that the order of corresponding
  angles in both triangles is the same.

triangle ABC triangle DEF
B
E
D
F
A
C
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Triangle RST triangle XYZ. Name the
corresponding sides of these triangles.
T
Z
R
S
X
Y

• Because RST XYZ that means angle R angle X,
  angle S angle Y, and angle T angle Z.
• Now we write the following
• Angle R Angle X, so ST corresponds to YZ.
• Angle S Angle Y, so RT corresponds to XZ.
• Angle T Angle Z, so RS corresponds to XY.

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In similar triangles, corresponding sides are in
proportion that is, the ratios of their length
are equal. As shown below in the example triangle
ABC DEF, therefore we have the following
B

• AB BC AC
• DE EF DF
• 6 8 4 18
• 3 4 2 9

8 cm
6 cm
A
C
4 cm
E
2
4 cm
3 cm
D
F
1
2 cm
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Finding the Missing Sides of Similar Triangles

• To find a missing side of similar triangles
• 1.) write the ratios of the lengths of the
  corresponding
• sides
• 2.) write a proportion using a ratio with
  known terms
• and a ratio with an unknown term
• 3.) solve the proportion for the unknown term

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In the following diagram, triangle TAP triangle
RUN. Find x.

• Because TAP RUN, we write the ratios of the
  lengths of the corresponding sides.

A
N
x
15 cm
12 cm
9 cm
T
P
R
U
18 cm
30 cm
15 x

x 30 12 18
or
9 12

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Now cross multiply, then divide to get the length
of AP.
A
N
x
15 cm
12 cm
9 cm
T
P
R
U
18 cm
30 cm
15 x

9x 180 x 20 so x, or the length
of AP, is 20 cm
9 12

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THANK YOU
E
T
H
E
N
D