Warm-Up Exercises

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?

Warm-Up ExercisesEXAMPLE 1

Longest sides CAFD

43

1612 ==

Remaining sidesBCEF

43

12 9 ==

Shortest sides

Use the SSS Similarity Theorem

ABGH

88 == 1

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

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

Warm-Up ExercisesEXAMPLE 1 Use the SSS Similarity Theorem

Longest sides CAJG

1616 == 1

Remaining sides BCHJ

65

1210 ==

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

ANSWER

Warm-Up Exercises

SOLUTION

EXAMPLE 2 Use the SSS Similarity Theorem

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.

Warm-Up ExercisesEXAMPLE 2 Use the SSS Similarity Theorem

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 =AB

DEBCEF=

?

Warm-Up ExercisesEXAMPLE 2 Use the SSS Similarity Theorem

DF = 3(x + 1) = 24

824

412 =

ABDE

ACDF=

?

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

ANSWER

Warm-Up ExercisesGUIDED PRACTICE for Examples 1 and 2

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

MLN ~ ZYX.

ANSWER

Warm-Up ExercisesGUIDED PRACTICE for Examples 1 and 2

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

ANSWER 15, 16.5

Warm-Up ExercisesEXAMPLE 3 Use the SAS Similarity Theorem

Lean-to Shelter

You are building a lean-to shelter starting from a tree branch, as shown. Can you construct the right end so it is similar to the left end using the angle measure and lengths shown?

Warm-Up ExercisesEXAMPLE 3 Use the SAS Similarity Theorem

Both m A and m F equal = 53°, so A F. Next, compare the ratios of the lengths of the sides that include A and F.

~

SOLUTION

Shorter sides Longer sides

ABFG

32

96 ==

ACFH

32

1510 ==

The lengths of the sides that include A and F are proportional.

Warm-Up ExercisesEXAMPLE 3 Use the SAS Similarity Theorem

ANSWER

So, by the SAS Similarity Theorem, ABC ~ FGH. Yes, you can make the right end similar to the left end of the shelter.

Warm-Up ExercisesEXAMPLE 4 Choose a method

Tell what method you would use to show that the triangles are similar.

Find the ratios of the lengths of the corresponding sides.

Shorter sides Longer sides

SOLUTION

CACD

35

1830 ==

BCEC

35

915 ==

The corresponding side lengths are proportional. The included angles ACB and DCE are congruent because they are vertical angles. So, ACB ~ DCE by the SAS Similarity Theorem.

Warm-Up ExercisesGUIDED PRACTICE for Examples 3 and 4

3. SRT ~ PNQ

Explain how to show that the indicated triangles are similar.

ANSWER

R N and = = , therefore the

triangles are similar by the SAS Similarity Theorem.

SRPN

RTNQ

4 3

Warm-Up ExercisesGUIDED PRACTICE for Examples 3 and 4

4. XZW ~ YZX

Explain how to show that the indicated triangles are similar.

XZYZ

WZXZ

43= WX

XY= = WZX XZY and

therefore the triangles are similar by either SSSor SAS Similarity Theorems.

ANSWER

Warm-Up ExercisesDaily Homework Quiz

1. Verify that ABC ~ DEF for the given information.

ABC : AC = 6, AB = 9, BC = 12;

DEF : DF = 2, DE= 3, EF = 4

ANSWER

ACDF

ABDE

BCEF

31

== =

so ABC ~ DEF by the SSS Similarity Theorem.

. The ratios are equal,

Warm-Up ExercisesDaily Homework Quiz

2. Show that the triangles are similar and write a similarity statement. Explain your reasoning.

ANSWER

XYAB

YZBC

34= = and Y B . So XYZ ~ ABC =

by the SAS Similarity Theorem.