Download Assessment Lesson 6: Defining and Applying Similarity Assessment

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Lesson 6: Defining and Applying Similarity
6/*5tSIMILARITY, CONGRUENCE, AND PROOFS
Lesson 6: Defining and Applying Similarity
Assessment
5. Are the two triangles !Unit!2!Geometry!Triangle!Similarity!Quiz!
similar? Why or why not?
Assessment
!
C
1.!! 5. Are the two triangles similar? Why or why not?
A
!
C
!
B
A
!
B
!
E
!
!
E
D
!
!
a. Yes, they are similar because of the AA Similarity Statement.
D
!
!
b. Yes,
Yes, they
they are
are similar
similar because
because of
of the
the AA
ASASimilarity
Congruence
Statement.
a.
Statement.
!
No, they
similar
because
congruence
is not preserved.
b.c. Yes,
they are
are not
similar
because
of the
ASA Congruence
Statement.
!
!
d. No,
It cannot
be not
determined
if the triangles
are similar.
c.
they are
similar because
congruence
is not preserved.
!
!
d. It cannot be determined if the triangles are similar.
!
2.!! 6. Are the two triangles similar? Why or why not?
!
C
6. Are the two triangles similar? Why or why not?
!
B
!
C
!
B
!
F
D
!
F
!
D
!
E
!
!
E
!
A
!
a. Yes, they are
A similar because of the AA Similarity Statement.
!
!
NAME:
b. Yes,
Yes, they
they are
are similar
similar because
because of
of the
the AA
ASASimilarity
Congruence
Statement.
a.
Statement.
!
6/*5tSIMILARITY,
CONGRUENCE,
AND
PROOFS
No, they
not
similar
because
congruence
is not preserved.
!
b.c. Yes,
they are
are
similar
because
of
the
ASA
Congruence
Statement.
!
Lesson
6: Defining
and
Applying
Similarity
d. No,
It cannot
be not
determined
if the triangles
are similar.
c.
they are
similar because
congruence
is not preserved.
!
Assessment
!
d. It cannot be determined if the triangles are similar.
3.!! 7.
ABC has undergone a series of similarity transformations to produce EFG . Which of the
!
following statements is always true?
!
a. The angles of EFG are proportional to the angles of ABC .
!
continued
!
b. The angles of EFG are the same as the angles of ABC .
continued
!
!
c. The sides of EFG increase proportionally to the sides of ABC . CCGPS Analytic Geometry Teacher U1-367
© Walch Education
Resource
!
U1-367
d. The sides of EFG decrease proportionally to the sides of ABC .
!
© Walch Education
CCGPS Analytic Geometry Teacher Resource
!
8. Identify the similar triangles.
E
9. Identify the similar triangles. Find x.
4.!!
C
!
D
x
!
6
2
9
!
A
NAME:
!
E
B
!6/*5tSIMILARITY, CONGRUENCE, AND PROOFS
F
!
Lesson
7: Proving Similarity
1
!
x
=
a.
△
ABC
∼△
FED
;
x
=
3
c.
△
ABC
∼△
FED
;
!
Assessment
3
!
1
! Progress
b. Assessment
△ ABC ∼△ DEF ; x = 3
d. △ ABC ∼△ DEF ; x =
! Circle the letter of the best answer.
3
!
5.! 1. Which statement would justify △ ABC ∼△ DEF ?
continued
!
!
A
!
U1-368
D
CCGPS Analytic Geometry Teacher Resource
© Walch Education
14
!
7
!
E
!
B
5
!
!
6
!
10
F
!
!
12
!
!
!
C
!
!
!
a. Angle-Angle (AA) Similarity Statement
!
b. Side-Angle-Side (SAS) Similarity Statement
!
!
c. Side-Side-Side (SSS) Similarity Statement
!
d. It is not possible to determine if △ ABC ∼△ DEF .
!
!
!
!
!
!
!
!
!
!
!
!
!!
!
continued
d. It is not possible to determine if △ ABC ∼△ DEF .
3. Which statement would justify △ ABC ∼△ DEF ?
6.!
!
15
A
B
!
!
10
D
E
!
!
!
12
!
7
!
!
!
F
C
!
!
a. Angle-Angle (AA) Similarity Statement
NAME:
!
b. Side-Angle-Side
(SAS) Similarity
!
6/*5tSIMILARITY,
CONGRUENCE,
AND Statement
PROOFS
!
continued
c. Side-Side-Side
Lesson 7: Proving
Similarity(SSS) Similarity Statement
!
d. It is not possible to determine if △ ABC ∼△ DEF .
Assessment
!
U1-457
! © Walch Education
CCGPS Analytic Geometry Teacher Resource
4.
△
ABF
∼△
ACE
.
What
is
the
length
of
CB
?
7.!!!!
!
C
!
x
!
B
!
!
!
12
!
!
A
!
9
5.4
E
F
!
!
a. 7.2 units
!
!
b. 4.05 units
!
c. 20 units
!
!
d. There is not enough information to determine the length of CB .
!
!
!
! 5. △ ABD ∼△ECD . What is the length of CD ?
!
B
!
!
C
!
30
!
x
!
!
!
!
D
6
18
A
E
a. 90 units
d. There is not enough information to determine the length of CB .
8.!5. △ ABD ∼△ECD . What is the length of CD ?
!
B
!
!
C
!
30
!
x
!
!
!
!
6
18
A
E
!
!
a. 90 units
!
! NAME: b. 7.5 units
! 6/*5tSIMILARITY, CONGRUENCE, AND PROOFS
c. 22.5 units
!
Lesson
7: Proving Similarity
!
d. There is not enough information to determine the length of CD .
!
!
2. Which statement would justify △ ABC ∼△ DEF ?
9.!
E
!
!
!
!
U1-458
!
CCGPS Analytic Geometry Teacher Resource
!
!
!
!
15
B
!
!
!
5
!
!
!
!
A
!
C
3 F
9
!
!
a. Angle-Angle (AA) Similarity Statement
!
b. Side-Angle-Side (SAS) Similarity Statement
!
!
c. Side-Side-Side (SSS) Similarity Statement
!
d. It is not possible to determine if △ ABC ∼△ DEF .
!
!
!
3. Which statement would justify △ ABC ∼△ DEF ?
!
15
A
B
!
!
D
12
D
Assessment
continued
© Walch Education
D
10
E
Read the scenario below and answer the questions that follow.
11. Suppose you are standing near a building and you want to know its height. The building casts a
10.!!!!
70-foot shadow. You cast a 4-foot shadow.
a. If you are 5 feet 6 inches tall, how tall is the building?
b. A nearby fence post is 3 feet tall. What is the approximate length of its shadow?
c. Explain how the Angle-Angle (AA) Similarity Statement helps you solve this problem.
U1-369
© Walch Education
CCGPS Analytic Geometry Teacher Resource