Algebra 1 Common Core Student Edition, Grade 8-9

Multiple Choice In the diagram,

A ABC ~ A DEF. What is DEI

(2 A 7.5

CIA 9-5

CCA 21.3

dA 24

• The length of AB, which The length o f DE

Xffln

Write a proportion involving

corresponds to DE. tw o pairs o f corre sp on d in g

• The lengths of two other sides: AB and DE, and BC
  co rre sp on d in g sides, and EF. The length o f DE is
  BC and EF the only unknown, so you can


• The triangles are similar. solve for it.

BC A B

W = DE ^r'te 3 ProPort'on-

if = W Substitute lengths.

16( DE) = 12(10) Cross Products Property

16DE = 120 Multiply.

DE = 7.5 Divide each side by 16 and simplify.

DE is 7.5. The correct answ er is A.

.j ) G o t It? 1. Use the figures in P roblem 1. W hat is AC?

,J W jo k
Is th e r e o n ly o n e
way to write a
proportion?
No. You can w rite
different proportions
to fin d th e h e ig h t. For
example, the follow ing
proportion also works.
building's shadow
girl's shadow ~
building's height
g irl’s height

You can also use p roportions to solve indirect m e asu rem en t problem s like finding a

distance using a m ap. You can use sim ilar figures an d p ro p o rtio n s to find lengths th at

you cannot measure directly.

Applying Similarity

Indirect M easurem en t The sun’s rays strike the

building and the girl at the same angle, forming the

two similar triangles shown. How tall is the building?

girl's shadow = girl's height Write a proportion,

b u i l d i n g s s h a d o w b u i l d i n g s h e ig h t

_3_

15

. 5
x

3x = 15(5)

3x = 75

x = 25

The building is 25 ft tall.

Substitute.

Cross Products

Property

Multiply.

Divide each side by 3.

rP o w e r A lg e b r a .c o m ^ Lesson 2-8 Pr o p o r t i o n s an d Si m i l ar Fig u r es^131

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