Similar Triangles 8.3. Identify similar triangles. homework Learn the definition of AA, SAS, SSS...
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![Page 1: Similar Triangles 8.3. Identify similar triangles. homework Learn the definition of AA, SAS, SSS similarity. Use similar triangles to solve problems.](https://reader033.fdocuments.net/reader033/viewer/2022061617/56649ea05503460f94ba38f0/html5/thumbnails/1.jpg)
Similar Triangles 8.3Similar Triangles 8.3
![Page 2: Similar Triangles 8.3. Identify similar triangles. homework Learn the definition of AA, SAS, SSS similarity. Use similar triangles to solve problems.](https://reader033.fdocuments.net/reader033/viewer/2022061617/56649ea05503460f94ba38f0/html5/thumbnails/2.jpg)
• Identify similar triangles.
homeworkhomework
• Learn the definition of AA, SAS, SSS similarity.
• Use similar triangles to solve problems.
![Page 3: Similar Triangles 8.3. Identify similar triangles. homework Learn the definition of AA, SAS, SSS similarity. Use similar triangles to solve problems.](https://reader033.fdocuments.net/reader033/viewer/2022061617/56649ea05503460f94ba38f0/html5/thumbnails/3.jpg)
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![Page 4: Similar Triangles 8.3. Identify similar triangles. homework Learn the definition of AA, SAS, SSS similarity. Use similar triangles to solve problems.](https://reader033.fdocuments.net/reader033/viewer/2022061617/56649ea05503460f94ba38f0/html5/thumbnails/4.jpg)
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![Page 5: Similar Triangles 8.3. Identify similar triangles. homework Learn the definition of AA, SAS, SSS similarity. Use similar triangles to solve problems.](https://reader033.fdocuments.net/reader033/viewer/2022061617/56649ea05503460f94ba38f0/html5/thumbnails/5.jpg)
Explain why the triangles are similar and write a similarity statement.
BCA ECD by the Vertical Angles Theorem. Also, A D by the Right Angle Congruence Theorem.
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Therefore ∆ABC ~ ∆DEC by AA Similarity.
![Page 6: Similar Triangles 8.3. Identify similar triangles. homework Learn the definition of AA, SAS, SSS similarity. Use similar triangles to solve problems.](https://reader033.fdocuments.net/reader033/viewer/2022061617/56649ea05503460f94ba38f0/html5/thumbnails/6.jpg)
D H by the Definition of Congruent Angles.
Therefore ∆DEF ~ ∆HJK by SAS Similarity.
Explain why the triangles are similar and write a similarity statement.
Arrange the sides by length so they correspond.
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![Page 7: Similar Triangles 8.3. Identify similar triangles. homework Learn the definition of AA, SAS, SSS similarity. Use similar triangles to solve problems.](https://reader033.fdocuments.net/reader033/viewer/2022061617/56649ea05503460f94ba38f0/html5/thumbnails/7.jpg)
Therefore ∆PQR ~ ∆STU by SSS similarity.
Explain why the triangles are similar and write a similarity statement.
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Arrange the sides by length so they correspond.
![Page 8: Similar Triangles 8.3. Identify similar triangles. homework Learn the definition of AA, SAS, SSS similarity. Use similar triangles to solve problems.](https://reader033.fdocuments.net/reader033/viewer/2022061617/56649ea05503460f94ba38f0/html5/thumbnails/8.jpg)
TXU VXW by the Vertical Angles Theorem.
Therefore ∆TXU ~ ∆VXW by SAS similarity.
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Explain why the triangles are similar and write a similarity statement.
Arrange the sides by length so they correspond.
![Page 9: Similar Triangles 8.3. Identify similar triangles. homework Learn the definition of AA, SAS, SSS similarity. Use similar triangles to solve problems.](https://reader033.fdocuments.net/reader033/viewer/2022061617/56649ea05503460f94ba38f0/html5/thumbnails/9.jpg)
Explain why the trianglesare similar and write asimilarity statement.
By the Triangle Sum Theorem, mC = 47°, so C F. B E by the Right Angle Congruence Theorem. Therefore, ∆ABC ~ ∆DEF by AA Similarity.
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![Page 10: Similar Triangles 8.3. Identify similar triangles. homework Learn the definition of AA, SAS, SSS similarity. Use similar triangles to solve problems.](https://reader033.fdocuments.net/reader033/viewer/2022061617/56649ea05503460f94ba38f0/html5/thumbnails/10.jpg)
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Determine if the triangles are similar, if so write a similarity statement.
By the Definition of Isosceles, A C and P R. By the Triangle Sum Theorem, mB = 40°, mC = 70°, mP = 70°, and mR = 70°.
Therefore, ∆ABC ~ ∆DEF by AA Similarity.
![Page 11: Similar Triangles 8.3. Identify similar triangles. homework Learn the definition of AA, SAS, SSS similarity. Use similar triangles to solve problems.](https://reader033.fdocuments.net/reader033/viewer/2022061617/56649ea05503460f94ba38f0/html5/thumbnails/11.jpg)
A A by Reflexive Property, and B C since they are right angles.
Explain why ∆ABE ~ ∆ACD, and then find CD.
Prove triangles are similar.
Therefore ∆ABE ~ ∆ACD by AA similarity.
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x(9) = 5(12)
9x = 60
CD
AC
BE
AB
x
12
5
9
![Page 12: Similar Triangles 8.3. Identify similar triangles. homework Learn the definition of AA, SAS, SSS similarity. Use similar triangles to solve problems.](https://reader033.fdocuments.net/reader033/viewer/2022061617/56649ea05503460f94ba38f0/html5/thumbnails/12.jpg)
Explain why ∆RSV ~ ∆RTU and then find RT.
Prove triangles are similar.
It is given that S T. R R by Reflexive Property.
Therefore ∆RSV ~ ∆RTU by AA similarity.
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RT(8) = 10(12)
8RT = 120
RT = 15
![Page 13: Similar Triangles 8.3. Identify similar triangles. homework Learn the definition of AA, SAS, SSS similarity. Use similar triangles to solve problems.](https://reader033.fdocuments.net/reader033/viewer/2022061617/56649ea05503460f94ba38f0/html5/thumbnails/13.jpg)
Given RS || UT, RS = 4, RQ = x + 3, QT = 2x + 10, UT = 10, find RQ and QT.
Since because they are
alternate interior angles. By AA Similarity, ΔRSQ ~ ΔTUQ. Using the
definition of similar polygons,
RQ = 8; QT = 20
![Page 14: Similar Triangles 8.3. Identify similar triangles. homework Learn the definition of AA, SAS, SSS similarity. Use similar triangles to solve problems.](https://reader033.fdocuments.net/reader033/viewer/2022061617/56649ea05503460f94ba38f0/html5/thumbnails/14.jpg)
Determine if the triangles are similar, if so write a similarity statement.
Find the missing angles.
3545
100
AA Similar AEZ ~ REB
Check for proportional sides. 8.15
128.
20
16
SAS Similar AGU ~ BEF
Check for proportional sides. 6.6
46.
5.4
36.
3
2
SSS Similar ABC ~ FED
Check for proportional sides.
5.140
605.1
30
4545.1
22
32
Not Similar
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![Page 15: Similar Triangles 8.3. Identify similar triangles. homework Learn the definition of AA, SAS, SSS similarity. Use similar triangles to solve problems.](https://reader033.fdocuments.net/reader033/viewer/2022061617/56649ea05503460f94ba38f0/html5/thumbnails/15.jpg)
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Determine if the triangles are similar, if so write a similarity statement.
Sides do not correspond.
Not Similar.
Check for proportional sides.
26.138
483.1
24
323.1
18
24
Not Similar.AA Similar FGH ~ KJH
Vertical angles.
Alternate Interior angles.
Check for proportional sides.
5.140
605.1
30
4545.1
22
32
Not Similar.
Find the missing angles.
120
45
Not Similar.
Check for proportional sides.
5.24
102
3
6
Not Similar.
![Page 16: Similar Triangles 8.3. Identify similar triangles. homework Learn the definition of AA, SAS, SSS similarity. Use similar triangles to solve problems.](https://reader033.fdocuments.net/reader033/viewer/2022061617/56649ea05503460f94ba38f0/html5/thumbnails/16.jpg)
1. A
2. B
3. C
4. D
Given ABC~EDC, AB = 38.5, DE = 11, AC = 3x + 8, and
CE = x + 2, find AC and CE.
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2x
8x3
11
5.38
88x3377x5.38
11x5.5
2x
AC = 3x + 8 CE = x + 2AC = 3(2) + 8AC = 14 AC = 4
AC = 2 + 2
![Page 17: Similar Triangles 8.3. Identify similar triangles. homework Learn the definition of AA, SAS, SSS similarity. Use similar triangles to solve problems.](https://reader033.fdocuments.net/reader033/viewer/2022061617/56649ea05503460f94ba38f0/html5/thumbnails/17.jpg)
Each pair of triangles below are similar, find x.
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x
8
9
x2
72x2 2
36x2
6x
6x
39
24
4x2
93624x8x2 2 0960x8x2 2 0480x4x2 0)20x)(24x(
20x
![Page 18: Similar Triangles 8.3. Identify similar triangles. homework Learn the definition of AA, SAS, SSS similarity. Use similar triangles to solve problems.](https://reader033.fdocuments.net/reader033/viewer/2022061617/56649ea05503460f94ba38f0/html5/thumbnails/18.jpg)
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![Page 19: Similar Triangles 8.3. Identify similar triangles. homework Learn the definition of AA, SAS, SSS similarity. Use similar triangles to solve problems.](https://reader033.fdocuments.net/reader033/viewer/2022061617/56649ea05503460f94ba38f0/html5/thumbnails/19.jpg)
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![Page 20: Similar Triangles 8.3. Identify similar triangles. homework Learn the definition of AA, SAS, SSS similarity. Use similar triangles to solve problems.](https://reader033.fdocuments.net/reader033/viewer/2022061617/56649ea05503460f94ba38f0/html5/thumbnails/20.jpg)
AssignmentAssignment
Section 11 – 36Section 11 – 36