Chapter 6, Section 3: Similar Figures and Scale Drawings

Ratios Make Things Similar!

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

Side AB corresponds to side EF. So x/18 = 16/24

Write the CROSS PRODUCT.

Divide and Simplify to SOLVE for X. 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

Indirect Measurements• Similar Figures can be used to measure

things that are difficult to measure otherwise.

• Compare something you know the measurements of to something you don’t know the measurements of.

• PROPORTIONS!

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

woman casts a shadow of 4feet. 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 Is12.5 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.

The Flagpole is 28 feet tall.

Things That Are Scaled…• Model Trains • (Scale Models of Real Trains, Just Tinier!)• Model Cars• (Again, Scale Models of the Real Thing)• Maps• (Scale Drawings of the Earth)• Blue Prints (Which Are No Longer Blue)• (Scale Drawing of a Building)

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.

• Athens is about 60 miles from Atlanta.

Assignment #44

• Page 291-292: 5-18 all, 20-22 all.

• REMEMBER TO WRITE ALL OF YOUR UNITS!

• If you’re dealing with Gallons for Minute, write Gallon per Minute!