solution example 1 use the sss similarity theorem compare abc and def by finding ratios of...

SOLUTION

EXAMPLE 1 Use the SSS Similarity Theorem

Compare ABC and DEF by finding ratios of corresponding side lengths.

Shortest sidesABDE

43

86 ==

Is either DEF or GHJ similar to ABC?

EXAMPLE 1

Longest sides CAFD

43

1612 ==

Remaining sidesBCEF

43

12 9 ==

Compare ABC and GHJ by finding ratios of corresponding side lengths.

Shortest sides

Use the SSS Similarity Theorem

ABGH

88 == 1

All of the ratios are equal, so ABC ~ DEF.ANSWER


Longest sides CAJG

1616 == 1

Remaining sides BCHJ

65

1210 ==

The ratios are not all equal, so ABC and GHJ are not similar.

ANSWER

SOLUTION


ALGEBRA

Find the value of x that makes ABC ~ DEF.

STEP 1 Find the value of x that makes corresponding side lengths proportional.

412 = x –1

18 Write proportion.


4 18 = 12(x – 1)

72 = 12x – 12

7 = x

Cross Products Property

Simplify.

Solve for x.

Check that the side lengths are proportional when x = 7.

STEP 2

BC = x – 1 = 6

618

412 =

ABDE

BCEF=?


DF = 3(x + 1) = 24

824

412 =

ABDE

ACDF=?

When x = 7, the triangles are similar by the SSS Similarity Theorem.

ANSWER

GUIDED PRACTICE for Examples 1 and 2

1. Which of the three triangles are similar? Write a similarity statement.


SOLUTION

Compare MLN and RST by finding ratios of corresponding side lengths.

Shortest sides LM RS

56

2024 ==

Longest sides ST LN

3324=

Remaining sides LN RT

3630 = = 13

15

The ratios are not all equal, so LMN and RST are not similar.


Compare LMN and ZYX by finding ratios of corresponding side lengths.

Shortest sides

Remaining sides

Longest sides

LM YZ

23

2030 ==

23=LN

XZ 2639=

MN XZ

2436 = = 2

3

All of the ratios are equal, so MLN ~ ZYX.

ANSWER


2. The shortest side of a triangle similar to RST is 12 units long. Find the other side lengths of the triangle.

A B

C

12

x y

Find the value of x that makes corresponding side lengths proportional.

2412

= 30 x

Write proportion.

x = 15

Cross Products Property24x = 12 30


Again to find out y

2412

= 33y

Write proportion.

y = 16.5

Cross Products Property24y = 12 33

So x = AC = 15 and y = BC = 16.5

ANSWER

solution example 1 use the sss similarity theorem compare abc and def by finding ratios of...

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