SIMILAR FIGURESObjective: Learn to determine whether figures are similar, to use scale factors and to find missing dimensions in similar figure.

SIMILAR FIGURESWhat are Similar Figure? Similar figure are figures that have the same shape but not necessarily the same size. The symbol “~” means “is similar to”

A

B

C

E

D FThese are corresponding

angles

These are corresponding

angles

CORRESPONDING ANGLESWhat are Corresponding Angles? Corresponding angles are matching angles of two or more similar figures, in the same position.

A

B

C

E

DFThese are

corresponding angles

These are corresponding sides

CORRESPONDING SIDESWhat are Corresponding Sides? Corresponding sides are matching sides of two or more similar figures, in the same position.

A

B

C

These are corresponding

angles

These are corresponding sides

E

DF

SIMILAR FIGURESSimilar Figures

Two figures are similar if:• The measures of their

corresponding angles are equal• The ratios of the lengths of their

corresponding sides are proportional

The ratio formed by the corresponding sides is the scale factor

TRY THIS!!!A picture 4 in. tall and 9 in. wide is to be scaled to 2.5 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?To find the scale factor, divide the known height of the scaled

picture by the corresponding height of the original picture

height of scaled pic

height of original pic

2 5

4

. 6 25.

Then multiply the width of the original picture by the scale factor

6 25 9. 5 625.

The picture should be 5.625 in. wide.

TRY THIS!!!A company’s logo is in the shape of an isosceles triangle with two sides that are 2.4 in. long and one side that is 1.8 in. long. On billboard, the triangle in the logo has two sides that each 8 ft. long. What is the length of the third side of the triangle on the billboard? 2 4 1 8

8

. in . in

ft x ft

Find the cross productin (ft) on both sides

cancel

Solve for x

2 4 8 1 8. in x ft ft . in

6x

Write the proportion

2 4 8 1 8. x .2 4 14 4. x .

The third side of the triangle is 6 ft long

REMEMBER!

The following are matching, or corresponding:A and X

Remember!

AB and XY

BC and YZ

AC and XZ

A

C BZ Y

X

C and Z

B and Y

TRY THIS!!!Which rectangles are similar?

A B C2in

3in

3in

4in

4in

6in

Since the three figures are rectangles all the angles

are right angles.

Compare the ratios of corresponding sides to see if they are equal.

3

4

length of rect. A

length of rect. B

2

3

? width of rect. A

width of rect. B

9 8The ratios are not equal. Rectangle A is not similar to rectangle B

3

6

length of rect. A

length of rect. C

2

4

? width of rect. A

width of rect. C

12 12The ratios are equal. Rectangle A is similar to rectangle C or A~C

EXAMPLE 1:

EXAMPLE 2:

EXAMPLE 3: