3-5: PROPORTIONS AND SIMILAR FIGURESEssential Question: How can you use proportions to find a distance that is difficult to measure?

3-5: Proportions and Similar Figures In the diagram, ∆ABC and ∆FGH are

similar. Similar figures have the same shape but not necessarily the same size.The symbol ~ means is similar to.

In similar triangles, corresponding angles are congruent and corresponding sides are in proportion. The order of the letters indicates the corresponding angles/sides. If ∆ABC ~ ∆FGH, then the following are true A F B G C H

A A

F F

C C

H

B

H

B

G G

3-5: Proportions and Similar Figures In the figure below, ∆ABC ~ ∆DEF. Find

DE. DE corresponds to AB EF corresponds to BC

32(DE) = 24(27) 32(DE) = 648

÷32 ÷32 DE = 20.25

24

27 32

DE EF

AB BCDE

3-5: Proportions and Similar Figures Your Turn

Using the same figure, if AC = 14 cm, what is DF?

10.5 cm

3-5: Proportions and Similar Figures You can use proportions to find the dimensions of

objects that are difficult to measure directly. Example

A tree casts a shadow 7.5 ft long. A woman 5 ft tall casts a shadow 3 feet long. The triangles shown for the tree and woman are similar. How tall is the tree?

5(7.5) = 3x 37.5 = 3x 12.5 = x

5

3 7.5

object object

shadow shadowx

3-5: Proportions and Similar Figures Your Turn

A tree casts a 26 foot shadow. A boy standing nearby casts a 12 foot shadow. His height is 4.5 ft tall. How tall is the tree? 9.75 ft

A house casts a 56 foot shadow. A girl standing nearby casts a 7.2 foot shadow. Her height is 5.4 ft. What is the height of the house? 42 ft

3-5: Proportions and Similar Figures A scale drawing is an enlarged or

reduced drawing that is similar to an actual object or place. Floor plans, blueprints, and maps are all examples of scale drawings. The ratio of a distance in the drawing to the corresponding actual distance is the scale of the drawing.

3-5: Proportions and Similar Figures Example

The scale of the map is 1 inch : 10 miles. Approximately how far is it from Valkaria to Wabasso?

1x = 10(1.75) x = 17.5

Your Turn Find the actual distance from Grant

to Gifford. 21 miles

1 1.75

10

map map

actual actual

x

3-5: Proportions and Similar Figures Assignment

Worksheet 3-5 All problems