Chapter 6, Section 3: Similar Figures and Scale Drawings

2

3=

f

21

Warm Up: Solve each Proportion, Round to the Nearest Tenth Where Necessary. You may use your calculators.

3

8=

50

p

9

4=

15

z

16

3=

19

g

f = 14

p = 133.3

z = 6.7

g = 3.6

Similar FiguresFigures that are SIMILAR have the SAME

SHAPE, but NOT necessarily the same SIZE.

Similar Figures have the Same Angles and Sides they are called Corresponding AnglesCorresponding Angles and Corresponding Corresponding SidesSides.

Corresponding = The SameCorresponding = The Same

These Figures Are Similar

Z

Y

X

15

9

12

53°

37°

90°

C

A

10

6

8

53°

37°

90° B

The symbol ~ means “is similar to”.

To the right,

ΔABC ~ ΔXYZ.

Similar Figures Have Two Properties.

• The Corresponding angles have equal measures.

• The lengths of the corresponding sides are in proportion.

Example Problems• Parallelogram ABCD ~ parallelogram EFGH. Find the

value of X.

• Hint: Write a proportion for corresponding sides.

A B

CD

X

16E F

GH

18

24

Corresponding Sides go Together.

Write the CROSS PRODUCT.

X

18=

16

24

(X)(24) = (18)(16), X = 12

Try This…• Parallelogram KLMN is similar to parallelogram ABCD in the previous example. Find the value of Y.

• Remember, X = 12 on Parallelogram ABCD.

A B

CD

X

16 K L

MN

Y

21

Have Ms. D-H Check Your Work.

Indirect Measurements• Similar Figures can be used to measure

things that are difficult to measure otherwise.

• PROPORTIONS!

Indirect Measurements• A tree casts a shadow of 10 feet long. A 5 foot

woman casts a shadow of 4 feet. The triangle shown for the woman and her shadow is similar to the triangle shown for the tree and its shadow. How tall is the tree?

D

The tree is 12.5 feet tall.

REMEMBER TO KEEP YOUR RATIOS INLINE!!!

THIS compared to THAT.

THIS ANDAND THAT have to be in the same ORDER every TIME.

Try This One and Draw It Yourself

• A building is 70 feet high and casts a 150 foot shadow. A nearby flagpole casts a 60 foot shadow. Draw a picture/diagram of the building, the building’s shadow, the flagpole, and it’s shadow. Use the triangles created to find the height of the flagpole.

Check your answer with Ms. D-H

Scale Drawings

• Scale Drawings are enlarged or reduced drawings that are SIMILARSIMILAR to an ACTUAL object or place.

• The RATIO of a distance in the drawing (or representation) to the corresponding actual distance is the SCALE of the drawing.

Guess Where This Is…

This is the ratio for this Scale Representation!

Try This One…

• The scale of the map is 1 inch : 40 miles. About how far from Atlanta is Athens, if the map distance is 1.5 inches?

• Write a proportion.

• Write Cross Products.

• Simplify.

Practice Setting Up ProportionsCreate a proportion for each scenario, then solve.

1) An image on a slide is similar to its projected image. The slide is 35mm wide and 21 mm high. It’s projected image is 85cm wide. To the nearest centimeter, how high is the image?

2) The scale of a map is 1cm : 12 km. Find the actual distance for each map distance.

a. 1.5 cm b. 4.25 cm