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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,