ExamView - 7.2 Similar Polygons · PDF file7.2 Similar Polygons Quiz Answer Section MULTIPLE...
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Name: ________________________ Class: ___________________ Date: __________ ID: A 1 7.2 Similar Polygons Quiz Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Identify the pairs of congruent angles and corresponding sides. a. ∠B ≅∠D, ∠C ≅∠E , ∠A ≅∠F, EF AC = DF AB = DE BC = 3 4 b. ∠B ≅∠D, ∠C ≅∠E , ∠A ≅∠F, AC EF = AB DF = BC DE = 3 4 c. ∠B ≅∠D, ∠C ≅∠E , ∠A ≅∠F, EF AB = DF AC = DE BC = 1 2 d. ∠B ≅∠D, ∠C ≅∠E , ∠A ≅∠F, AC EF = DF AB = DE BC = 4 3 ____ 2. Determine whether the rectangles are similar. If so, write the similarity ratio and a similarity statement. a. The similarity ratio is 3 5 and rectangle MNOP ~ rectangle RSTU. b. Rectangles MNOP and RSTU are not similar. c. The similarity ratio is 2 5 and rectangle MNOP ~ rectangle RSTU. d. The similarity ratio is 2 3 and rectangle MNOP ~ rectangle RSTU.
Transcript of ExamView - 7.2 Similar Polygons · PDF file7.2 Similar Polygons Quiz Answer Section MULTIPLE...
Name: ________________________ Class: ___________________ Date: __________ ID: A
1
7.2 Similar Polygons Quiz
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Identify the pairs of congruent angles and corresponding sides.
a. ∠B ≅ ∠D, ∠C ≅ ∠E, ∠A ≅ ∠F, EF
AC=
DF
AB=
DE
BC=
3
4
b. ∠B ≅ ∠D, ∠C ≅ ∠E, ∠A ≅ ∠F, AC
EF=
AB
DF=
BC
DE=
3
4
c. ∠B ≅ ∠D, ∠C ≅ ∠E, ∠A ≅ ∠F, EF
AB=
DF
AC=
DE
BC=
1
2
d. ∠B ≅ ∠D, ∠C ≅ ∠E, ∠A ≅ ∠F, AC
EF=
DF
AB=
DE
BC=
4
3
____ 2. Determine whether the rectangles are similar. If so, write the similarity ratio and a similarity statement.
a. The similarity ratio is 3
5 and rectangle MNOP ~ rectangle RSTU.
b. Rectangles MNOP and RSTU are not similar.
c. The similarity ratio is 2
5 and rectangle MNOP ~ rectangle RSTU.
d. The similarity ratio is 2
3 and rectangle MNOP ~ rectangle RSTU.
Name: ________________________ ID: A
2
____ 3. Maya is making a miniature dinner table for her little sister. She wants the table top to be similar to their real
dinner table top. Find the width of the miniature table top to the nearest tenth of a centimeter.
a. 4.9 cm
b. 18.3 cm
c. 0.2 cm
d. 0.3 cm
____ 4. A video game designer is modeling a tower that is 320 ft high and 260 ft wide. She creates a model so that
the similarity ratio of the model to the tower is 1
500. What is the height and the width of the model in inches?
a. height = 0.64 in.; width = 0.52 in.
b. height = 3840 in.; width = 3120 in.
c. height = 7.68 in.; width = 6.24 in.
d. height = 160,000 in.; width = 130,000 in.
ID: A
1
7.2 Similar Polygons Quiz
Answer Section
MULTIPLE CHOICE
1. ANS: A
∠B ≅ ∠D and ∠C ≅ ∠E. By the Third Angles Theorem ∠A ≅ ∠F.
EF
AC=
6
8=
3
4
DF
AB=
9
12=
3
4
DE
BC=
13.5
18=
3
4
Feedback
A Correct!
B Does AC/EF equal 3/4?
C Are EF and AB corresponding sides?
D Make sure the ratios compare corresponding sides. AC/EF equals 4/3 but DF/AB does
not equal 4/3.
PTS: 1 DIF: Basic REF: 1b7bc30e-4683-11df-9c7d-001185f0d2ea
OBJ: 7-2.1 Describing Similar Polygons STA: NY.NYLES.MTH.05.GEO.G.RP.2
LOC: MTH.C.11.08.03.01.001 | MTH.C.11.08.03.01.002 | MTH.C.11.08.03.005
TOP: 7-2 Ratios in Similar Polygons KEY: similar polygons |corresponding sides
DOK: DOK 1
ID: A
2
2. ANS: A
Step 1 Identify pairs of congruent angles.
∠M ≅ ∠R, ∠N ≅ ∠S ,
∠O ≅ ∠T and ∠P ≅ ∠U
All angles of a rectangle are right angles and are
congruent.
Step 2 Compare corresponding sides.
MN
RS=
9
15=
3
5
MP
RU=
6
10=
3
5
Thus the similarity ratio is 3
5, and rectangle MNOP ~ rectangle RSTU.
Feedback
A Correct!
B Identify pairs of congruent angles, then compare corresponding sides.
C Make sure each ratio compares a side from one rectangle with the corresponding side
from the second rectangle.
D Make sure each ratio compares a side from one rectangle with the corresponding side
from the second rectangle.
PTS: 1 DIF: Basic REF: 1b7dfe5a-4683-11df-9c7d-001185f0d2ea
OBJ: 7-2.2 Identifying Similar Polygons STA: NY.NYLES.MTH.05.GEO.G.RP.2
LOC: MTH.C.11.08.03.002 | MTH.C.11.08.03.004 TOP: 7-2 Ratios in Similar Polygons
KEY: similar polygons | similarity statement DOK: DOK 1
ID: A
3
3. ANS: A
x is the width of the miniature in centimeters. The rectangular miniature is similar to the rectangular table
top, so the corresponding lengths are proportional.
length of dinner table top
length of miniature=
width of dinner table top
width of miniature
2.5
9.5=
1.3
x
2.5x = (1.3)(9.5) Cross Product Property
2.5x = 12.35 Simplify.
x ≈ 4.9 Divide both sides by 2.5.
The width of the miniature table top is about 4.9 cm.
Feedback
A Correct!
B When you work with proportions, be sure the ratios compare corresponding measures.
C What does the Cross Product Property state?
D Make sure each ratio compares the rectangles in the same order.
PTS: 1 DIF: Average REF: 1b8060b6-4683-11df-9c7d-001185f0d2ea
OBJ: 7-2.3 Application LOC: MTH.C.09.03.01.001 | MTH.C.11.08.03.006
TOP: 7-2 Ratios in Similar Polygons KEY: similar figures | side length
DOK: DOK 2
4. ANS: C
Step 1 Convert measurements to inches.
tower’s length = 320 ft = 3840 in.
tower’s width = 260 ft = 3120 in.
Step 2 Apply the scale factor formula.
new dimension = (scale factor)(original dimension)
model’s length =1
500
Ê
ËÁÁÁ
ˆ
¯˜̃˜ 3840 in.( ) = 7.68 in.
model’s width =1
500
Ê
ËÁÁÁ
ˆ
¯˜̃˜ 3120 in.( ) = 6.24 in.
Feedback
A Convert answers to inches.
B Multiply the scale factor by each dimension.
C Correct!
D Multiply the scale factor by each dimension.
PTS: 1 DIF: Advanced REF: 1b8087c6-4683-11df-9c7d-001185f0d2ea
LOC: MTH.C.11.08.03.005 | MTH.C.11.08.03.006 TOP: 7-2 Ratios in Similar Polygons
KEY: application | similarity ratio | scale model DOK: DOK 2
Name: ________________________ Class: ___________________ Date: __________ ID: B
1
7.2 Similar Polygons Quiz
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Maya is making a miniature dinner table for her little sister. She wants the table top to be similar to their real
dinner table top. Find the width of the miniature table top to the nearest tenth of a centimeter.
a. 4.9 cm
b. 18.3 cm
c. 0.3 cm
d. 0.2 cm
____ 2. Identify the pairs of congruent angles and corresponding sides.
a. ∠B ≅ ∠D, ∠C ≅ ∠E, ∠A ≅ ∠F, EF
AC=
DF
AB=
DE
BC=
3
4
b. ∠B ≅ ∠D, ∠C ≅ ∠E, ∠A ≅ ∠F, AC
EF=
DF
AB=
DE
BC=
4
3
c. ∠B ≅ ∠D, ∠C ≅ ∠E, ∠A ≅ ∠F, EF
AB=
DF
AC=
DE
BC=
1
2
d. ∠B ≅ ∠D, ∠C ≅ ∠E, ∠A ≅ ∠F, AC
EF=
AB
DF=
BC
DE=
3
4
Name: ________________________ ID: B
2
____ 3. A video game designer is modeling a tower that is 180 ft high and 160 ft wide. She creates a model so that
the similarity ratio of the model to the tower is 1
500. What is the height and the width of the model in inches?
a. height = 2160 in.; width = 1920 in.
b. height = 4.32 in.; width = 3.84 in.
c. height = 0.36 in.; width = 0.32 in.
d. height = 90,000 in.; width = 80,000 in.
____ 4. Determine whether the rectangles are similar. If so, write the similarity ratio and a similarity statement.
a. Rectangles MNOP and RSTU are not similar.
b. The similarity ratio is 3
5 and rectangle MNOP ~ rectangle RSTU.
c. The similarity ratio is 2
5 and rectangle MNOP ~ rectangle RSTU.
d. The similarity ratio is 2
3 and rectangle MNOP ~ rectangle RSTU.
ID: B
1
7.2 Similar Polygons Quiz
Answer Section
MULTIPLE CHOICE
1. ANS: A
x is the width of the miniature in centimeters. The rectangular miniature is similar to the rectangular table
top, so the corresponding lengths are proportional.
length of dinner table top
length of miniature=
width of dinner table top
width of miniature
2.5
9.5=
1.3
x
2.5x = (1.3)(9.5) Cross Product Property
2.5x = 12.35 Simplify.
x ≈ 4.9 Divide both sides by 2.5.
The width of the miniature table top is about 4.9 cm.
Feedback
A Correct!
B When you work with proportions, be sure the ratios compare corresponding measures.
C Make sure each ratio compares the rectangles in the same order.
D What does the Cross Product Property state?
PTS: 1 DIF: Average REF: 1b8060b6-4683-11df-9c7d-001185f0d2ea
OBJ: 7-2.3 Application LOC: MTH.C.09.03.01.001 | MTH.C.11.08.03.006
TOP: 7-2 Ratios in Similar Polygons KEY: similar figures | side length
DOK: DOK 2
ID: B
2
2. ANS: A
∠B ≅ ∠D and ∠C ≅ ∠E. By the Third Angles Theorem ∠A ≅ ∠F.
EF
AC=
6
8=
3
4
DF
AB=
9
12=
3
4
DE
BC=
13.5
18=
3
4
Feedback
A Correct!
B Make sure the ratios compare corresponding sides. AC/EF equals 4/3 but DF/AB does
not equal 4/3.
C Are EF and AB corresponding sides?
D Does AC/EF equal 3/4?
PTS: 1 DIF: Basic REF: 1b7bc30e-4683-11df-9c7d-001185f0d2ea
OBJ: 7-2.1 Describing Similar Polygons STA: NY.NYLES.MTH.05.GEO.G.RP.2
LOC: MTH.C.11.08.03.01.001 | MTH.C.11.08.03.01.002 | MTH.C.11.08.03.005
TOP: 7-2 Ratios in Similar Polygons KEY: similar polygons |corresponding sides
DOK: DOK 1
3. ANS: B
Step 1 Convert measurements to inches.
tower’s length = 180 ft = 2160 in.
tower’s width = 160 ft = 1920 in.
Step 2 Apply the scale factor formula.
new dimension = (scale factor)(original dimension)
model’s length =1
500
Ê
ËÁÁÁ
ˆ
¯˜̃˜ 2160 in.( ) = 4.32 in.
model’s width =1
500
Ê
ËÁÁÁ
ˆ
¯˜̃˜ 1920 in.( ) = 3.84 in.
Feedback
A Multiply the scale factor by each dimension.
B Correct!
C Convert answers to inches.
D Multiply the scale factor by each dimension.
PTS: 1 DIF: Advanced REF: 1b8087c6-4683-11df-9c7d-001185f0d2ea
LOC: MTH.C.11.08.03.005 | MTH.C.11.08.03.006 TOP: 7-2 Ratios in Similar Polygons
KEY: application | similarity ratio | scale model DOK: DOK 2
ID: B
3
4. ANS: B
Step 1 Identify pairs of congruent angles.
∠M ≅ ∠R, ∠N ≅ ∠S ,
∠O ≅ ∠T and ∠P ≅ ∠U
All angles of a rectangle are right angles and are
congruent.
Step 2 Compare corresponding sides.
MN
RS=
9
15=
3
5
MP
RU=
6
10=
3
5
Thus the similarity ratio is 3
5, and rectangle MNOP ~ rectangle RSTU.
Feedback
A Identify pairs of congruent angles, then compare corresponding sides.
B Correct!
C Make sure each ratio compares a side from one rectangle with the corresponding side
from the second rectangle.
D Make sure each ratio compares a side from one rectangle with the corresponding side
from the second rectangle.
PTS: 1 DIF: Basic REF: 1b7dfe5a-4683-11df-9c7d-001185f0d2ea
OBJ: 7-2.2 Identifying Similar Polygons STA: NY.NYLES.MTH.05.GEO.G.RP.2
LOC: MTH.C.11.08.03.002 | MTH.C.11.08.03.004 TOP: 7-2 Ratios in Similar Polygons
KEY: similar polygons | similarity statement DOK: DOK 1
Name: ________________________ Class: ___________________ Date: __________ ID: C
1
7.2 Similar Polygons Quiz
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Maya is making a miniature dinner table for her little sister. She wants the table top to be similar to their real
dinner table top. Find the width of the miniature table top to the nearest tenth of a centimeter.
a. 0.3 cm
b. 0.2 cm
c. 4.9 cm
d. 18.3 cm
____ 2. A video game designer is modeling a tower that is 240 ft high and 180 ft wide. She creates a model so that
the similarity ratio of the model to the tower is 1
500. What is the height and the width of the model in inches?
a. height = 5.76 in.; width = 4.32 in.
b. height = 2880 in.; width = 2160 in.
c. height = 0.48 in.; width = 0.36 in.
d. height = 120,000 in.; width = 90,000 in.
Name: ________________________ ID: C
2
____ 3. Identify the pairs of congruent angles and corresponding sides.
a. ∠B ≅ ∠D, ∠C ≅ ∠E, ∠A ≅ ∠F, EF
AC=
DF
AB=
DE
BC=
3
4
b. ∠B ≅ ∠D, ∠C ≅ ∠E, ∠A ≅ ∠F, EF
AB=
DF
AC=
DE
BC=
1
2
c. ∠B ≅ ∠D, ∠C ≅ ∠E, ∠A ≅ ∠F, AC
EF=
AB
DF=
BC
DE=
3
4
d. ∠B ≅ ∠D, ∠C ≅ ∠E, ∠A ≅ ∠F, AC
EF=
DF
AB=
DE
BC=
4
3
____ 4. Determine whether the rectangles are similar. If so, write the similarity ratio and a similarity statement.
a. Rectangles MNOP and RSTU are not similar.
b. The similarity ratio is 3
5 and rectangle MNOP ~ rectangle RSTU.
c. The similarity ratio is 2
5 and rectangle MNOP ~ rectangle RSTU.
d. The similarity ratio is 2
3 and rectangle MNOP ~ rectangle RSTU.
ID: C
1
7.2 Similar Polygons Quiz
Answer Section
MULTIPLE CHOICE
1. ANS: C
x is the width of the miniature in centimeters. The rectangular miniature is similar to the rectangular table
top, so the corresponding lengths are proportional.
length of dinner table top
length of miniature=
width of dinner table top
width of miniature
2.5
9.5=
1.3
x
2.5x = (1.3)(9.5) Cross Product Property
2.5x = 12.35 Simplify.
x ≈ 4.9 Divide both sides by 2.5.
The width of the miniature table top is about 4.9 cm.
Feedback
A Make sure each ratio compares the rectangles in the same order.
B What does the Cross Product Property state?
C Correct!
D When you work with proportions, be sure the ratios compare corresponding measures.
PTS: 1 DIF: Average REF: 1b8060b6-4683-11df-9c7d-001185f0d2ea
OBJ: 7-2.3 Application LOC: MTH.C.09.03.01.001 | MTH.C.11.08.03.006
TOP: 7-2 Ratios in Similar Polygons KEY: similar figures | side length
DOK: DOK 2
ID: C
2
2. ANS: A
Step 1 Convert measurements to inches.
tower’s length = 240 ft = 2880 in.
tower’s width = 180 ft = 2160 in.
Step 2 Apply the scale factor formula.
new dimension = (scale factor)(original dimension)
model’s length =1
500
Ê
ËÁÁÁ
ˆ
¯˜̃˜ 2880 in.( ) = 5.76 in.
model’s width =1
500
Ê
ËÁÁÁ
ˆ
¯˜̃˜ 2160 in.( ) = 4.32 in.
Feedback
A Correct!
B Multiply the scale factor by each dimension.
C Convert answers to inches.
D Multiply the scale factor by each dimension.
PTS: 1 DIF: Advanced REF: 1b8087c6-4683-11df-9c7d-001185f0d2ea
LOC: MTH.C.11.08.03.005 | MTH.C.11.08.03.006 TOP: 7-2 Ratios in Similar Polygons
KEY: application | similarity ratio | scale model DOK: DOK 2
3. ANS: A
∠B ≅ ∠D and ∠C ≅ ∠E. By the Third Angles Theorem ∠A ≅ ∠F.
EF
AC=
6
8=
3
4
DF
AB=
9
12=
3
4
DE
BC=
13.5
18=
3
4
Feedback
A Correct!
B Are EF and AB corresponding sides?
C Does AC/EF equal 3/4?
D Make sure the ratios compare corresponding sides. AC/EF equals 4/3 but DF/AB does
not equal 4/3.
PTS: 1 DIF: Basic REF: 1b7bc30e-4683-11df-9c7d-001185f0d2ea
OBJ: 7-2.1 Describing Similar Polygons STA: NY.NYLES.MTH.05.GEO.G.RP.2
LOC: MTH.C.11.08.03.01.001 | MTH.C.11.08.03.01.002 | MTH.C.11.08.03.005
TOP: 7-2 Ratios in Similar Polygons KEY: similar polygons |corresponding sides
DOK: DOK 1
ID: C
3
4. ANS: B
Step 1 Identify pairs of congruent angles.
∠M ≅ ∠R, ∠N ≅ ∠S ,
∠O ≅ ∠T and ∠P ≅ ∠U
All angles of a rectangle are right angles and are
congruent.
Step 2 Compare corresponding sides.
MN
RS=
9
15=
3
5
MP
RU=
6
10=
3
5
Thus the similarity ratio is 3
5, and rectangle MNOP ~ rectangle RSTU.
Feedback
A Identify pairs of congruent angles, then compare corresponding sides.
B Correct!
C Make sure each ratio compares a side from one rectangle with the corresponding side
from the second rectangle.
D Make sure each ratio compares a side from one rectangle with the corresponding side
from the second rectangle.
PTS: 1 DIF: Basic REF: 1b7dfe5a-4683-11df-9c7d-001185f0d2ea
OBJ: 7-2.2 Identifying Similar Polygons STA: NY.NYLES.MTH.05.GEO.G.RP.2
LOC: MTH.C.11.08.03.002 | MTH.C.11.08.03.004 TOP: 7-2 Ratios in Similar Polygons
KEY: similar polygons | similarity statement DOK: DOK 1
