1. Similar Triangles 8.3

2. Identify similar triangles.
Learn the definition of AA, SAS, SSS similarity.
Use similar triangles to solve problems.
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5. BCA  ECD by the Vertical Angles Theorem.
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.
Therefore ∆ABC ~ ∆DEC by AA Similarity.
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6. D  H by the Definition of Congruent Angles.
Explain why the triangles are similar and write a similarity statement.
D  H by the Definition of Congruent Angles.
Arrange the sides by length so they correspond.
Therefore ∆DEF ~ ∆HJK by SAS Similarity.
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7. Arrange the sides by length so they correspond.
Explain why the triangles are similar and write a similarity statement.
Arrange the sides by length so they correspond.
Therefore ∆PQR ~ ∆STU by SSS similarity.
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8. TXU  VXW by the Vertical Angles Theorem.
Explain why the triangles are similar and write a similarity statement.
TXU  VXW by the Vertical Angles Theorem.
Arrange the sides by length so they correspond.
Therefore ∆TXU ~ ∆VXW by SAS similarity.
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9. Explain why the triangles are similar and write a
similarity statement.
By the Triangle Sum Theorem, mC = 47°, so C  F. B  E by the Right Angle Congruence Theorem.
Therefore, ∆ABC ~ ∆DEF by AA Similarity.
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10. Therefore, ∆ABC ~ ∆DEF by AA Similarity.
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, mB = 40°, mC = 70°, mP = 70°, and mR = 70°.
Therefore, ∆ABC ~ ∆DEF by AA Similarity.
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11. Explain why ∆ABE ~ ∆ACD, and then find CD.
Prove triangles are similar.
A  A by Reflexive Property, and
B  C since they are right angles.
Therefore ∆ABE ~ ∆ACD by AA similarity.
x(9) = 5(12)
9x = 60
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12. 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.
RT(8) = 10(12)
8RT = 120
RT = 15
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13. 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

14. Determine if the triangles are similar, if so write a similarity statement.
35
45
100
Find the missing angles.
Check for proportional sides.
AA Similar AEZ ~ REB
SAS Similar AGU ~ BEF
Check for proportional sides.
Check for proportional sides.
SSS Similar ABC ~ FED
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Not Similar

15. Determine if the triangles are similar, if so write a similarity statement.
Alternate Interior angles.
Vertical angles.
Check for proportional sides.
Sides do not correspond.
Not Similar.
AA Similar FGH ~ KJH
Not Similar.
Find the missing angles.
120
45
Check for proportional sides.
Check for proportional sides.
Not Similar.
Not Similar.
Not Similar.
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16. Given ABC~EDC, AB = 38.5, DE = 11, AC = 3x + 8, and CE = x + 2, find AC and CE.
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17. Each pair of triangles below are similar, find x.
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20. Assignment
Section 11 – 36