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Objective
Determine whether figures are similar
and find a missing length in a pair of
similar figures
Vocabulary
Similar Figures
Figures that have the same shape but not
necessarily the same size
Vocabulary
Indirect measurement
Finding a measurement by using similar
triangles and writing a proportion
Vocabulary
Proportion
An equation that shows that two ratios are
equivalent
Math Symbols
Is similar to

Example 1 Find Side Measures of Similar Triangles
Example 2 Use Indirect Measurement
If ABC  DEF, find the length of
Small
Large
=
Triangles are similar so start
with a proportion
To set up determine what you
are working with
Small triangle and a large
triangle
1/2
If ABC  DEF, find the length of
Small 3
=
Large 4.5
Find a side on each triangle
that is similar
On the first ratio, put 3 with
the small triangle
On the first ratio, put 4.5 with
the large triangle
1/2
If ABC  DEF, find the length of
Small 3
=
x
Large 4.5
Define the variable
Since DF is on the large
triangle, place the variable in
the denominator
Find the side similar to DF on
the small triangle
1/2
If ABC  DEF, find the length of
Small 3
11
=
x
Large 4.5
Since 11 is with the small
triangle, place 11 in the
numerator
Solve for x by using cross
multiplication
1/2
If ABC  DEF, find the length of
Small 3
11
=
x
Large 4.5
3x = 4.5(11)
3x = 49.5
3
3
Cross multiply
Combine “like” terms
Ask “What is being done to
the variable?”
The variable is being
multiplied by 3
Do the inverse on both sides
of the equal sign
Using a fraction bar, divide
both sides by 3
1/2
If ABC  DEF, find the length of
Small 3
11
=
x
Large 4.5
3x = 4.5(11)
3x = 49.5
3
3
1  x = 16.5
x = 16.5
Combine “like” terms
Use the Identity Property to
multiply 1  x
The question asked to find
the length of DF
Add dimensional analysis
Answer: DF = 16.5 cm
1/2
If JKL  MNO, find the length of
Answer: JL = 13.5 in
1/2
A rectangular picture window 12-feet long and 6-feet wide
needs to be shortened to 9 feet in length to fit a redesigned
wall. If the architect wants the new window to be similar to
the old window, how wide will the new window be?
6 ft
12 ft
Small
Large
=
x ft
9 ft
Draw a picture of the two windows
and put in the dimensions
Set up the proportion
Make the first ratio with similar
sides from each window
2/2
A rectangular picture window 12-feet long and 6-feet wide
needs to be shortened to 9 feet in length to fit a redesigned
wall. If the architect wants the new window to be similar to
the old window, how wide will the new window be?
6 ft
12 ft
Small 9
=
Large 12
x
x ft
9 ft
The small window length is 9 ft
The large window length is 12 ft
Define the variable
The new window is the small
window
2/2
A rectangular picture window 12-feet long and 6-feet wide
needs to be shortened to 9 feet in length to fit a redesigned
wall. If the architect wants the new window to be similar to
the old window, how wide will the new window be?
6 ft
12 ft
Small 9
=
Large 12
x
6
x ft
9 ft
The similar wide is the width of
the large window
Find the value of x by cross
multiplying
2/2
A rectangular picture window 12-feet long and 6-feet wide
needs to be shortened to 9 feet in length to fit a redesigned
wall. If the architect wants the new window to be similar to
the old window, how wide will the new window be?
Cross multiply
Small 9 = x
6
Large 12
Combine “like” terms
12x = 9(6)
12x = 54
12
12
Ask “What is being done to
the variable?”
The variable is being
multiplied by 12
Do the inverse on both sides
of the equal sign
Using a fraction bar, divide
both sides by 12
2/2
A rectangular picture window 12-feet long and 6-feet wide
needs to be shortened to 9 feet in length to fit a redesigned
wall. If the architect wants the new window to be similar to
the old window, how wide will the new window be?
Combine “like” terms
Small 9 = x
6
Large 12
Use the Identity Property to
multiply 1  x
12x = 9(6)
Add dimensional analysis
12x = 54
12 12
1  x = 4.5
Answer:
x = 4.5 ft
2/2
*
Tom has a rectangular garden which has a length of 12
feet and a width of 8 feet. He wishes to start a second
garden which is similar to the first and will have a width
of 6 feet. Find the length of the new garden. Draw the
gardens and label dimensions
Answer: x = 9 ft
2/2
Assignment
Lesson 10:6
Similar Figures
3 - 12 All