1. Splash Screen

2. Five-Minute Check (over Lesson 7–2) Then/Now
Postulate 7.1: Angle-Angle (AA) Similarity
Example 1: Use the AA Similarity Postulate
Theorems
Proof: Theorem 7.2
Example 2: Use the SSS and SAS Similarity Theorems
Example 3: Standardized Test Example
Theorem 7.4: Properties of Similarity
Example 4: Parts of Similar Triangles
Example 5: Real-World Example: Indirect Measurement
Concept Summary: Triangle Similarity
Lesson Menu

3. A B Determine whether the triangles are similar.
A. Yes, corresponding angles are congruent and corresponding sides are proportional.
B. No, corresponding sides are not proportional. A B
5-Minute Check 1

4. The quadrilaterals are similar
The quadrilaterals are similar. Find the scale factor of the larger quadrilateral to the smaller quadrilateral.
A. 5:3
B. 4:3
C. 3:2
D. 2:1 A B C D
5-Minute Check 2

5. A B C D The triangles are similar. Find x and y. A. x = 5.5, y = 12.9
B. x = 8.5, y = 9.5
C. x = 5, y = 7.5
D. x = 9.5, y = 8.5 A B C D
5-Minute Check 3

6. __
Two pentagons are similar with a scale factor of The perimeter of the larger pentagon is 42 feet. What is the perimeter of the smaller pentagon? 3 7
A. 12 ft
B. 14 ft
C. 16 ft
D. 18 ft A B C D
5-Minute Check 4

7. Use similar triangles to solve problems.
You used the AAS, SSS, and SAS Congruence Theorems to prove triangles congruent. (Lesson 4–4)
Identify similar triangles using the AA Similarity Postulate and the SSS and SAS Similarity Theorems.
Use similar triangles to solve problems.
Then/Now

8. Concept

9. Use the AA Similarity Postulate
A. Determine whether the triangles are similar. If so, write a similarity statement. Explain your reasoning.
Example 1

10. By the Triangle Sum Theorem, 42 + 58 + mA = 180, so mA = 80.
Use the AA Similarity Postulate
Since mB = mD, B D
By the Triangle Sum Theorem, mA = 180, so mA = 80.
Since mE = 80, A E.
Answer: So, ΔABC ~ ΔDEC by the AA Similarity.
Example 1

11. Use the AA Similarity Postulate
B. Determine whether the triangles are similar. If so, write a similarity statement. Explain your reasoning.
Example 1

12. QXP NXM by the Vertical Angles Theorem.
Use the AA Similarity Postulate
QXP NXM by the Vertical Angles Theorem.
Since QP || MN, Q N.
Answer: So, ΔQXP ~ ΔNXM by the AA Similarity.
Example 1

13. A. Determine whether the triangles are similar
A. Determine whether the triangles are similar. If so, write a similarity statement.
A. Yes; ΔABC ~ ΔFGH
B. Yes; ΔABC ~ ΔGFH
C. Yes; ΔABC ~ ΔHFG
D. No; the triangles are not similar. A B C D
Example 1

14. B. Determine whether the triangles are similar
B. Determine whether the triangles are similar. If so, write a similarity statement.
A. Yes; ΔWVZ ~ ΔYVX
B. Yes; ΔWVZ ~ ΔXVY
C. Yes; ΔWVZ ~ ΔXYV
D. No; the triangles are not similar. A B C D
Example 1

15. Concept

16. Answer: So, ΔABC ~ ΔDEC by the SSS Similarity Theorem.
Use the SSS and SAS Similarity Theorems
A. Determine whether the triangles are similar. If so, write a similarity statement. Explain your reasoning.
Answer: So, ΔABC ~ ΔDEC by the SSS Similarity Theorem.
Example 2

17. By the Reflexive Property, M  M.
Use the SSS and SAS Similarity Theorems
B. Determine whether the triangles are similar. If so, write a similarity statement. Explain your reasoning.
By the Reflexive Property, M  M.
Answer: Since the lengths of the sides that include M are proportional, ΔMNP ~ ΔMRS by the SAS Similarity Theorem.
Example 2

18. A. Determine whether the triangles are similar
A. Determine whether the triangles are similar. If so, choose the correct similarity statement to match the given data.
A. ΔPQR ~ ΔSTR by SSS Similarity Theorem
B. ΔPQR ~ ΔSTR by SAS Similarity Theorem
C. ΔPQR ~ ΔSTR by AAA Similarity Theorem
D. The triangles are not similar. A B C D
Example 2

19. B. Determine whether the triangles are similar
B. Determine whether the triangles are similar. If so, choose the correct similarity statement to match the given data.
A. ΔAFE ~ ΔABC by SSS Similarity Theorem
B. ΔAFE ~ ΔACB by SSS Similarity Theorem
C. ΔAFE ~ ΔAFC by SSS Similarity Theorem
D. ΔAFE ~ ΔBCA by SSS Similarity Theorem A B C D
Example 2

20. If ΔRST and ΔXYZ are two triangles such that = which of the following would be sufficient to prove that the triangles are similar? A B C R  S D __ 2 3
___ RS XY
Example 3

21. Read the Test Item
You are given that = and asked to identify which additional information would be sufficient to prove that ΔRST ~ ΔXYZ. __ 2 3
___ RS XY
Example 3

22. __ 2 3
Solve the Test Item
Since = , you know that these two sides are proportional at the scale factor of Check each answer choice until you find one that supplies sufficient information to prove that ΔRST ~ ΔXYZ.
___ RS XY
Example 3

23. __ 2 3
Choice A
If = , then you know that the other two sides are proportional. You do not, however, know whether that scale factor is as determined by Therefore, this is not sufficient information.
___ RT XZ ST YZ RS XY
Example 3

24. __ 2 3
Choice B
If = = , then you know that all the sides are proportional by the same scale factor, This is sufficient information by the SSS Similarity Theorem to determine that the triangles are similar.
___ RS XY RT XZ
Answer: B
Example 3

25. A B C D A. = B. mA = 2mD C. = D. = AC DC 4 3 BC 5 EC
Given ΔABC and ΔDEC, which of the following would be sufficient information to prove the triangles are similar?
A =
B. mA = 2mD
C =
D =
___ AC DC __ 4 3 BC 5 EC A B C D
Example 3

26. Parts of Similar Triangles
ALGEBRA Given , RS = 4, RQ = x + 3, QT = 2x + 10, UT = 10, find RQ and QT.
Example 4

27. Cross Products Property
Parts of Similar Triangles
Since because they are alternate interior angles. By AA Similarity, ΔRSQ ~ ΔTUQ. Using the definition of similar polygons,
Substitution
Cross Products Property
Example 4

28. Distributive Property
Parts of Similar Triangles
Distributive Property
Subtract 8x and 30 from each side.
Divide each side by 2.
Now find RQ and QT.
Answer: RQ = 8; QT = 20
Example 4

29. ALGEBRA Given AB = 38.5, DE = 11, AC = 3x + 8, and CE = x + 2, find AC.
Example 4

30. Concept

31. P 479 9, 11, 14, 16 – 20 even