Algebra 1 Common Core Student Edition, Grade 8-9

Proportions and

Similar Figures

Common Core State Standards

A-CED.A.1 Create equations... in one variable and use

them to solve problems. Include equations arising from

lin e a r ... functions. Also A-REI.B.3

MP 1, MP 2, MP 3, MP4, MP 6

Objectives To find m issing lengths in sim ilar figures

To use sim ilar figures w h en m easu rin g indirectly

c\LV£ j.

A good model is

an e x a c t copy o f

the thing th a t it

represents. It's

ju st a d iffe re n t

size.

V

MATHEMAIICAL

PRACTICES

Lesso n

Vocabulary

sim ilar f ig u r es

• scale drawing


• scale


• scale model

In th e Solve It, the sailboat an d its m odel have th e sam e shape b u t they are different

sizes. Similar figures have th e sam e shape b u t n o t necessarily th e sam e size.

Essential U nderstanding You can use p ro p o rtio n s to find m issing side lengths

in sim ilar figures. Such figures can help you m easu re real-w orld distances indirectly.

The symbol ~ m ean s “is sim ilar to.” In th e diagram , A ABC ~ A FGH.

F

A

H

In sim ilar figures, the m easures of corresponding angles are equal, a n d corresponding

side lengths are in proportion. The order of th e letters w h en you n am e sim ilar figures

is im p o rtan t because it tells w hich p arts of the figures are corresponding parts. So,

because AABC ~ A FGH, the following is true.

AA = AF A B = AG AC = AH and

The sym bol = means "is congruent to."

Congruent angles have the same measure.

AB

FG

A

AC __ BC

FH GH

A_

The ratios are equal.

130 Chapter 2 So l v i n g Eq u a t i o n s

Lilfe!