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Similar Triangles 8.3. Identify similar triangles. homework Learn the definition of AA, SAS, SSS...

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Similar Triangles Similar Triangles 8.3 8.3
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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.

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.

• 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.

homeworkhomework

Page 4: Similar Triangles 8.3. Identify similar triangles. homework Learn the definition of AA, SAS, SSS similarity. Use similar triangles to solve problems.

homeworkhomework

Page 5: Similar Triangles 8.3. Identify similar triangles. homework Learn the definition of AA, SAS, SSS similarity. Use similar triangles to solve problems.

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.

homeworkhomework

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.

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.

homeworkhomework

Page 7: Similar Triangles 8.3. Identify similar triangles. homework Learn the definition of AA, SAS, SSS similarity. Use similar triangles to solve problems.

Therefore ∆PQR ~ ∆STU by SSS similarity.

Explain why the triangles are similar and write a similarity statement.

homeworkhomework

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.

TXU VXW by the Vertical Angles Theorem.

Therefore ∆TXU ~ ∆VXW by SAS similarity.

homeworkhomework

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.

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.

homeworkhomework

Page 10: Similar Triangles 8.3. Identify similar triangles. homework Learn the definition of AA, SAS, SSS similarity. Use similar triangles to solve problems.

homeworkhomework

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.

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.

homeworkhomework

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.

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.

homeworkhomework

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.

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.

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

homeworkhomework

Page 15: Similar Triangles 8.3. Identify similar triangles. homework Learn the definition of AA, SAS, SSS similarity. Use similar triangles to solve problems.

homeworkhomework

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.

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.

homeworkhomework

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.

Each pair of triangles below are similar, find x.

homeworkhomework

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.

homeworkhomework

Page 19: Similar Triangles 8.3. Identify similar triangles. homework Learn the definition of AA, SAS, SSS similarity. Use similar triangles to solve problems.

homeworkhomework

Page 20: Similar Triangles 8.3. Identify similar triangles. homework Learn the definition of AA, SAS, SSS similarity. Use similar triangles to solve problems.

AssignmentAssignment

Section 11 – 36Section 11 – 36


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