Transcript 5-5: Using Similar Figures

5-7: Similar Figures
Using proportions for dimensional
analysis and problem solving
Vocabulary
Polygon
A closed figure made up of 3 or more line segments.
Similar Figures
Figures that have the same shape, but not necessarily the same size.
Corresponding sides
The sides of two or more polygons that are in the same relative
position.
Corresponding angles
The angles of two or more polygons that are in the same relative
position.
Examples
A)
B)
10 ÷ 6 = 1.6666…
18 ÷ 10.8 = 1.6666…
21 ÷ 12.6 = 1.6666…
Steps in Solving
To determine if two figures are similar…
I. Determine if the corresponding angles are
equal and/or the corresponding sides are
proportional.
Steps in Solving
To determine if two figures are similar…
I. Determine if the corresponding angles are
equal and/or the corresponding sides are
proportional.
A)
B)
Steps in Solving
To find the missing lengths of two similar polygons…
I.
Write a proportion using the given corresponding lengths and
missing length.
• Be sure to place the corresponding lengths, in the corresponding
position in the proportion.
II. Use cross multiplication, or other strategies to solve the
proportion.
Steps in Solving
To find the missing lengths of two similar polygons…
I.
Write a proportion using the given corresponding lengths and
missing length.
• Be sure to place the corresponding lengths, in the corresponding
position in the proportion.
II. Use cross multiplication, or other strategies to solve the
proportion.
C)
Steps in Solving
Scale Factor
The ratio formed by the corresponding sides of two or more
similar figures.
Steps in Solving
Scale Factor
The ratio formed by the corresponding sides of two or more
similar figures.
D) Find the Scale Factor of the two similar triangles.
Scale Factor:______________
Steps in Solving
Scale Factor
The ratio formed by the corresponding sides of two or more
similar figures.
E) A picture 10 in tall and 14 in. wide is to be scaled to 1.5
in. tall to be displayed on a Web page. How wide
should the picture be on the Web page for the two
pictures to be similar? Use the Scale Factor to solve.
Now try these…
1) A 5 ft person near a tree has a shadow of 12 ft long. The tree has
a shadow of 42 ft long. What is the height of tree? (Drawing a
rough sketch helps is solving).
2) The scale on a map is 1 inch = 20 miles. The distance from
Fairfield to Hartford is 2.5 inches how many miles it from Fairfield to
Hartford?
3) On a map 1 inch represents 25 miles. You measure the distance
between two cities on a map and find the distance to be 5 ½
inches. Find the number of miles between the cities.