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Splash Screen. 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 - PowerPoint PPT Presentation
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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
Over Lesson 7–2
A. A
B. B
A. Yes, corresponding angles are congruent and corresponding sides are proportional.
B. No, corresponding sides are not proportional.
Determine whether the triangles are similar.
Over Lesson 7–2
A. A
B. B
C. C
D. D
A. 5:3
B. 4:3
C. 3:2
D. 2:1
The quadrilaterals are similar. Find the scale factor of the larger quadrilateral to the smaller quadrilateral.
Over Lesson 7–2
A. A
B. B
C. C
D. D
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
The triangles are similar.Find x and y.
Over Lesson 7–2
A. A
B. B
C. C
D. D
A. 12 ft
B. 14 ft
C. 16 ft
D. 18 ft
__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?
37
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.
Use the AA Similarity Postulate
A. Determine whether the triangles are similar. If so, write a similarity statement. Explain your reasoning.
Use the AA Similarity Postulate
Since mB = mD, B D
By the Triangle Sum Theorem, 42 + 58 + mA = 180, so mA = 80.
Since mE = 80, A E.
Answer: So, ΔABC ~ ΔDEC by the AA Similarity.
Use the AA Similarity Postulate
B. Determine whether the triangles are similar. If so, write a similarity statement. Explain your reasoning.
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.
A. A
B. B
C. C
D. D
A. Yes; ΔABC ~ ΔFGH
B. Yes; ΔABC ~ ΔGFH
C. Yes; ΔABC ~ ΔHFG
D. No; the triangles are not similar.
A. Determine whether the triangles are similar. If so, write a similarity statement.
A. A
B. B
C. C
D. D
A. Yes; ΔWVZ ~ ΔYVX
B. Yes; ΔWVZ ~ ΔXVY
C. Yes; ΔWVZ ~ ΔXYV
D. No; the triangles are not similar.
B. Determine whether the triangles are similar. If so, write a similarity statement.
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.
Use the SSS and SAS Similarity Theorems
B. Determine whether the triangles are similar. If so, write a similarity statement. Explain your reasoning.
Answer: Since the lengths of the sides that include M are proportional, ΔMNP ~ ΔMRS by the SAS Similarity Theorem.
By the Reflexive Property, M M.
A. A
B. B
C. C
D. D
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. Determine whether the triangles are similar. If so, choose the correct similarity statement to match the given data.
A. A
B. B
C. C
D. D
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
B. Determine whether the triangles are similar. If so, choose the correct similarity statement to match the given data.
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
__23
___RSXY
Read the Test Item
You are given that = and asked to identify which
additional information would be sufficient to prove that
ΔRST ~ ΔXYZ.
__23
___RSXY
__23
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.
__23
___RSXY
__23
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.
___RTXZ
___STYZ
___RSXY
__23
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.
___RSXY
___RTXZ
___RTXZ
Answer: B
A. A
B. B
C. C
D. D
Given ΔABC and ΔDEC, which of the following would be sufficient information to prove the triangles are similar?
A. =
B. mA = 2mD
C. =
D. =
___ACDC
___ACDC
__43
___BCDC
__45
___BCEC
Parts of Similar Triangles
ALGEBRA Given , RS = 4, RQ = x + 3, QT = 2x + 10, UT = 10, find RQ and QT.
Parts of Similar Triangles
Substitution
Cross Products Property
Since
because they are alternate interior angles. By AA
Similarity, ΔRSQ ~ ΔTUQ. Using the definition of similar
polygons,
Parts of Similar Triangles
Answer: RQ = 8; QT = 20
Distributive Property
Subtract 8x and 30 from each side.
Divide each side by 2.
Now find RQ and QT.
A. A
B. B
C. C
D. D
A. 2
B. 4
C. 12
D. 14
ALGEBRA Given AB = 38.5, DE = 11, AC = 3x + 8, and CE = x + 2, find AC.