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