Similar Triangles 8.3Similar Triangles 8.3

• Identify similar triangles.

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• Learn the definition of AA, SAS, SSS similarity.

• Use similar triangles to solve problems.

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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.

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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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.

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.

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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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.

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

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

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

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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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.

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

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

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AssignmentAssignment

Section 11 – 36Section 11 – 36