AR 4'2 Solving multistep problems involving distance'

1
Similar Figures
and
Scale Drawings

• AR 4.2 Solving multi-step problems involving
  distance.
• MG 1.2 Construct and read scale drawings.
• MG 1.3 Use proportions and dimensions to find
  indirect measurement.

2
Using Similar Figures
Similar Figures

• ________________ have the same shape, but NOT
  necessarily the same size.
• Similar figures have __________________ and
  _________________ .
• The symbol means ___________.

corresponding angles
corresponding sides
is similar to
This symbol is called a tilde.
3
Similar Figures
X

• At the right,
• ?ABC ?XYZ.

53
corresponding angles
9
A
53
6
Y
15
B
10
12
8
37
37
corresponding sides
Z
C
4
Two Properties of Similar Figures
X

• Corresponding angles have equal measures.

53
corresponding angles
9
A
53
6
Y
15
B
10
12
8
37
37
Z
C
5
Two Properties of Similar Figures
X

• Lengths of corresponding sides are in proportion.

53
9
A
53
6
Y
15
B
10
12
8
37
37
corresponding sides
Z
C
6
Example 1 GEOMETRY CONNECTION

• Parallelogram ABCD parallelogram EFGH.
• Find the value of x.

16
16
B
A
x
x
C
D
24
24
F
E
18
18
G
H
7
Try This

• Parallelogram KLMN is similar to parallelogram
  ABCD. Find the value of y.

16
B
A
12
C
D
21
L
K
y
M
N
8
Try This Solution

• Parallelogram KLMN is similar to parallelogram
  ABCD. Find the value of y.

16
16
B
A
12
12
C
D
21
21
L
K
y
M
N
9
Example 2 GEOMETRY CONNECTION

• Indirect Measurement A tree casts a shadow 10
  ft. long. A 5-ft woman casts a shadow 4 ft long.
  The triangle shown for the woman and her shadow
  is similar to the triangle shown for the tree and
  its shadow.
• How tall is tree?

10
Example 2 GEOMETRY CONNECTION

• Indirect Measurement A tree casts a shadow 10
  ft. long. A 5-ft woman casts a shadow 4 ft long.
  The triangle shown for the woman and her shadow
  is similar to the triangle shown for the tree and
  its shadow.
• How tall is tree?

10 ft
11
Example 2 GEOMETRY CONNECTION

• Indirect Measurement A tree casts a shadow 10
  ft. long. A 5 ft woman casts a shadow 4 ft long.
  The triangle shown for the woman and her shadow
  is similar to the triangle shown for the tree and
  its shadow.
• How tall is tree?

5 ft
10 ft
12
Example 2 GEOMETRY CONNECTION

• Indirect Measurement A tree casts a shadow 10
  ft. long. A 5-ft woman casts a shadow 4 ft long.
  The triangle shown for the woman and her shadow
  is similar to the triangle shown for the tree and
  its shadow.
• How tall is tree?

4 ft
5 ft
10 ft
13
Example 2 GEOMETRY CONNECTION

• Indirect Measurement A tree casts a shadow 10
  ft. long. A 5-ft woman casts a shadow 4 ft long.
  The triangle shown for the woman and her shadow
  is similar to the triangle shown for the tree and
  its shadow.
• How tall is tree?

x ft
5 ft
4 ft
10 ft
14
Example 2 GEOMETRY CONNECTION

• Indirect Measurement A tree casts a shadow 10
  ft. long. A 5-ft woman casts a shadow 4 ft long.
  The triangle shown for the woman and her shadow
  is similar to the triangle shown for the tree and
  its shadow.
• How tall is tree?

x ft
5 ft
4 ft
10 ft
15
Example 2 INDIRECT MEASUREMENT

• Corresponding sides of similar triangles are in
  proportion.
• Write cross products.
• Divide each side by 4
• Simplify

x
5
The tree is 12.5 ft tall.
4
10
16
Try This

• Indirect Measurement A building 70 ft high casts
  a 150 ft shadow. A nearby flagpole casts a 60 ft
  shadow. Draw a diagram. Use similar triangles
  to find the height of the flagpole.