6.5 prove triangles similar by sss and sas
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Transcript of 6.5 prove triangles similar by sss and sas
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6.56.5 Prove Triangles Similar by SSS and SASBell Thinger
ANSWER not similar
Determine whether the two triangles are similar.1. ABC: m A = 90º, m B = 44º; DEF : m D = 90º,
m E = 46º.
2. ABC: m A = 132º, m B = 24º; DEF : m D = 90º, m F = 24º.
ANSWER similar
ANSWER 5
3. Solve = .12
6 x – 1 8
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6.5
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6.5Example 1
SOLUTION
Compare ABC and DEF by finding ratios of corresponding side lengths.
Shortest sides
=ABDE
43
86=
Is either DEF or GHJ similar to ABC?
Longest sides
CAFD
43
1612 ==
Remaining sides
BCEF
43
12 9 ==
All of the ratios are equal, so ABC ~ DEF.
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6.5
Shortest sides
ABGH
88 == 1
Compare ABC and GHJ by finding ratios of corresponding side lengths.
Longest sides
CAJG
1616 == 1
Remaining sides
BCHJ
65
1210 ==
The ratios are not all equal, so ABC and GHJ are not similar.
Example 1
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6.5Example 2
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.
72 = 12x – 12
7 = x
Cross Products Property
Simplify.
Solve for x.
4 18 = 12(x – 1).
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6.5
Check that the side lengths are proportional when x = 7.
STEP 2
BC = x – 1 = 6
618
412 =AB
DEBCEF=
?
DF = 3(x + 1) = 24
824
412 =
ABDE
ACDF=
?
When x = 7, the triangles are similar by the SSS Similarity Theorem.
Example 2
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6.5Guided Practice
1. Which of the three triangles are similar? Write a similarity statement.
MLN ~ ZYX
ANSWER
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6.5
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
Guided Practice
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6.5Example 3
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?
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6.5
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 sidesABFG
32
96 ==
ACFH
32
1510 ==
The lengths of the sides that include A and F are proportional.
So, by the SAS Similarity Theorem, ABC ~ FGH. Yes, you can make the right end similar to the left end of the shelter.
Example 3
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6.5Example 4
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.
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6.5Guided Practice
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
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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
Guided Practice
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6.5CONCEPT SUMMARY
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6.5Exit Slip
1. Verify that ABC ~ DEF for the given information.
ABC : AC = 6, AB = 9, BC = 12;
DEF : DF = 2, DE= 3, EF = 4
ANSWER
= =DFAC
DEAB
EFBC
13=
so ABC ~ DEF by the SSS Similarity Theorem.
. The ratios are equal,
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6.5
2. Show that the triangles are similar and write a similarity statement. Explain your reasoning.
ANSWER
= =ABXY
BCYZ
43 and Y B . So XYZ ~ ABC
by the SAS Similarity Theorem.
Exit Slip
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ANSWER 7.5
3. Find the length of BC.
Exit Slip
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6.5
4. A tree casts a shadow that is 30 feet long. At the same time a person standing nearby, who is five feet two inches tall, casts a shadow that is 50 inches long. How tall is the tree to the nearest foot?
37 ftANSWER
Exit Slip
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No ANSWERANSWER Yes; XYZ ~ CBA
Exit Slip
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Homework
Pg 409-413#5, 6, 10, 12, 33