Name: ________________________ Class: ___________________ Date: __________
ID: A
7.4-7.5 Similar Triangles and Proportionality Quiz
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Find NP .
a.
b.
c.
d.
____
2. Find BD .
a.
____
NP = 1
NP = 1.25
NP = 1.6
NP = 2
BD = 5
b.
BD = 22
c.
BD = 10
d.
BD = 12
3. A tree is standing next to a 40-foot high building. The tree has an 18-foot shadow, while the building has a
16-foot shadow. How tall is the tree, rounded to the nearest foot?
a. 45 feet
b. 36 feet
c. 42 feet
d. 7 feet
1
Name: ________________________
ID: A
Short Answer
BONUS
1. Given ∆ABC ∼ ∆JKL, find the perimeter and area of ∆JKL.
Perimeter = ________________________
Area = ___________________________
2
ID: A
7.4-7.5 Similar Triangles and Proportionality Quiz
Answer Section
MULTIPLE CHOICE
1. ANS: B
It is given that PR Ä NQ, so
2
PN
=
5
8
8(PN) = 10
PN = 1.25
RQ
PN
=
by the Triangle Proportionality Theorem.
NM
QM
Substitute 2 for RQ, 8 for QM, and 5 for NM.
Cross Products Property
Divide by 8.
Feedback
A
B
C
D
Use the Triangle Proportionality Theorem to find the length.
Correct!
Use the Triangle Proportionality Theorem to find the length.
Use the Triangle Proportionality Theorem to find the length.
PTS:
OBJ:
STA:
LOC:
TOP:
DOK:
1
DIF: Average
REF: 1b89ea26-4683-11df-9c7d-001185f0d2ea
7-4.1 Finding the Length of a Segment
NY.NYLES.MTH.05.GEO.G.G.46 | NY.NYLES.MTH.05.GEO.G.G.67
MTH.C.11.01.02.01.001 | MTH.C.11.08.03.04.002
7-4 Applying Properties of Similar Triangles
KEY: similar triangles | segment length
DOK 2
1
ID: A
2. ANS: D
Since AD bisects ∠BAC ,
18 3x − 3
=
15 x + 5
18(x + 5) = 15(3x − 3)
18x + 90 = 45x − 45
135 = 27x
x=5
BD = 3x − 3
BD = 3(5) − 3
BD = 12
AB BD
=
by the Triangle Angle Bisector Theorem.
AC CD
Substitute the given values.
Cross Products Property
Distributive Property
Simplify.
Divide.
Substitute for x.
Simplify.
Feedback
A
B
C
D
This is the value of x, now find the value of BD.
This is the value of BC, now find the value of BD.
This is the value of CD, now find the value of BD.
Correct!
PTS:
OBJ:
TOP:
DOK:
1
DIF: Average
REF: 1b8eaede-4683-11df-9c7d-001185f0d2ea
7-4.4 Using the Triangle Angle Bisector Theorem
LOC: MTH.C.11.08.03.04.008
7-4 Applying Properties of Similar Triangles
KEY: triangle angle bisector theorem
DOK 2
2
ID: A
3. ANS: A
Because the sun’s rays are parallel, we know that ∠J ≅ ∠C .
Therefore ∆ABC ∼ ∆GHJ by AA similarity.
The height of the tree is the length of GH .
AB GH
=
Corresponding sides are proportional.
GJ
AC
40 GH
=
Substitute.
18
16
(40)(18) = 16(GH)
Cross Products Property
45 = GH
Divide both sides by 16.
The height of the tree is 45 feet.
Feedback
A
B
C
D
Correct!
Set up the proportions. Compare height to height and shadow to shadow.
Set up the proportions. Compare height to height and shadow to shadow.
Set up the proportions. Compare height to height and shadow to shadow.
PTS:
OBJ:
LOC:
KEY:
1
DIF: Basic
7-5.1 Application
MTH.C.09.03.006
indirect measurement | similar
REF:
NAT:
TOP:
DOK:
3
1b91384a-4683-11df-9c7d-001185f0d2ea
NT.CCSS.MTH.10.9-12.G.SRT.5
7-5 Using Proportional Relationships
DOK 2
ID: A
SHORT ANSWER
1. ANS:
P = 42 ft, A = 40.5 ft 2
For the two triangles the similarity ratio is
18
12
3
, or 2 .
3
By the Proportional Perimeters and Areas Theorem, the ratio of the triangles’ perimeters is also 2 , and the
Ê 3 ˆ2 9
ratios of their areas is ÁÁÁ 2 ˜˜˜ = 4 .
Ë ¯
Perimeter:
P
3
=
Set up the ratio.
28 2
2(P) = (28)(3)
Cross Products Property
P = 42 feet
Simplify.
Area:
A 9
=
18 4
4(A) = (18)(9)
A = 40.5 feet 2
PTS:
OBJ:
LOC:
KEY:
1
DIF: Average
REF: 1b95fd02-4683-11df-9c7d-001185f0d2ea
7-5.4 Using Ratios to Find Perimeters and Areas
NAT: NT.CCSS.MTH.10.9-12.G.SRT.5
MTH.C.09.01.02.005
TOP: 7-5 Using Proportional Relationships
similarity ratio | proportion | similar triangles | area
DOK: DOK 2
4
Name: ________________________ Class: ___________________ Date: __________
ID: B
7.4-7.5 Similar Triangles and Proportionality Quiz
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Find NP .
a.
b.
c.
d.
NP = 2
NP = 1
NP = 1.6
NP = 1.25
____
2. A tree is standing next to a 40-foot high building. The tree has an 18-foot shadow, while the building has a
16-foot shadow. How tall is the tree, rounded to the nearest foot?
a. 7 feet
b. 45 feet
c. 36 feet
d. 42 feet
____
3. Find BD .
a.
BD = 22
b.
BD = 5
c.
1
BD = 10
d.
BD = 12
Name: ________________________
ID: B
Short Answer
BONUS
1. Given ∆ABC ∼ ∆JKL, find the perimeter and area of ∆JKL.
Perimeter = ________________________
Area = ___________________________
2
ID: B
7.4-7.5 Similar Triangles and Proportionality Quiz
Answer Section
MULTIPLE CHOICE
1. ANS: D
It is given that PR Ä NQ, so
PN
2
=
8
5
8(PN) = 10
PN = 1.25
RQ
PN
=
by the Triangle Proportionality Theorem.
NM
QM
Substitute 2 for RQ, 8 for QM, and 5 for NM.
Cross Products Property
Divide by 8.
Feedback
A
B
C
D
Use the Triangle Proportionality Theorem to find the length.
Use the Triangle Proportionality Theorem to find the length.
Use the Triangle Proportionality Theorem to find the length.
Correct!
PTS:
OBJ:
STA:
LOC:
TOP:
DOK:
1
DIF: Average
REF: 1b89ea26-4683-11df-9c7d-001185f0d2ea
7-4.1 Finding the Length of a Segment
NY.NYLES.MTH.05.GEO.G.G.46 | NY.NYLES.MTH.05.GEO.G.G.67
MTH.C.11.01.02.01.001 | MTH.C.11.08.03.04.002
7-4 Applying Properties of Similar Triangles
KEY: similar triangles | segment length
DOK 2
1
ID: B
2. ANS: B
Because the sun’s rays are parallel, we know that ∠J ≅ ∠C .
Therefore ∆ABC ∼ ∆GHJ by AA similarity.
The height of the tree is the length of GH .
AB GH
=
Corresponding sides are proportional.
GJ
AC
40 GH
=
Substitute.
16
18
(40)(18) = 16(GH)
Cross Products Property
45 = GH
Divide both sides by 16.
The height of the tree is 45 feet.
Feedback
A
B
C
D
Set up the proportions. Compare height to height and shadow to shadow.
Correct!
Set up the proportions. Compare height to height and shadow to shadow.
Set up the proportions. Compare height to height and shadow to shadow.
PTS:
OBJ:
LOC:
KEY:
1
DIF: Basic
7-5.1 Application
MTH.C.09.03.006
indirect measurement | similar
REF:
NAT:
TOP:
DOK:
2
1b91384a-4683-11df-9c7d-001185f0d2ea
NT.CCSS.MTH.10.9-12.G.SRT.5
7-5 Using Proportional Relationships
DOK 2
ID: B
3. ANS: D
Since AD bisects ∠BAC ,
18 3x − 3
=
15 x + 5
18(x + 5) = 15(3x − 3)
18x + 90 = 45x − 45
135 = 27x
x=5
BD = 3x − 3
BD = 3(5) − 3
BD = 12
AB BD
=
by the Triangle Angle Bisector Theorem.
AC CD
Substitute the given values.
Cross Products Property
Distributive Property
Simplify.
Divide.
Substitute for x.
Simplify.
Feedback
A
B
C
D
This is the value of BC, now find the value of BD.
This is the value of x, now find the value of BD.
This is the value of CD, now find the value of BD.
Correct!
PTS:
OBJ:
TOP:
DOK:
1
DIF: Average
REF: 1b8eaede-4683-11df-9c7d-001185f0d2ea
7-4.4 Using the Triangle Angle Bisector Theorem
LOC: MTH.C.11.08.03.04.008
7-4 Applying Properties of Similar Triangles
KEY: triangle angle bisector theorem
DOK 2
3
ID: B
SHORT ANSWER
1. ANS:
P = 42 ft, A = 40.5 ft 2
For the two triangles the similarity ratio is
18
12
3
, or 2 .
3
By the Proportional Perimeters and Areas Theorem, the ratio of the triangles’ perimeters is also 2 , and the
Ê 3 ˆ2 9
ratios of their areas is ÁÁÁ 2 ˜˜˜ = 4 .
Ë ¯
Perimeter:
P
3
=
Set up the ratio.
28 2
2(P) = (28)(3)
Cross Products Property
P = 42 feet
Simplify.
Area:
A 9
=
18 4
4(A) = (18)(9)
A = 40.5 feet 2
PTS:
OBJ:
LOC:
KEY:
1
DIF: Average
REF: 1b95fd02-4683-11df-9c7d-001185f0d2ea
7-5.4 Using Ratios to Find Perimeters and Areas
NAT: NT.CCSS.MTH.10.9-12.G.SRT.5
MTH.C.09.01.02.005
TOP: 7-5 Using Proportional Relationships
similarity ratio | proportion | similar triangles | area
DOK: DOK 2
4
Name: ________________________ Class: ___________________ Date: __________
ID: C
7.4-7.5 Similar Triangles and Proportionality Quiz
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Find BD .
a.
____
b.
BD = 22
c.
BD = 12
d.
BD = 10
2. Find NP .
a.
b.
c.
d.
____
BD = 5
NP = 2
NP = 1.25
NP = 1.6
NP = 1
3. A tree is standing next to a 40-foot high building. The tree has an 18-foot shadow, while the building has a
16-foot shadow. How tall is the tree, rounded to the nearest foot?
a. 45 feet
b. 7 feet
c. 42 feet
d. 36 feet
1
Name: ________________________
ID: C
Short Answer
BONUS
1. Given ∆ABC ∼ ∆JKL, find the perimeter and area of ∆JKL.
Perimeter = ________________________
Area = ___________________________
2
ID: C
7.4-7.5 Similar Triangles and Proportionality Quiz
Answer Section
MULTIPLE CHOICE
1. ANS: C
Since AD bisects ∠BAC ,
18 3x − 3
=
15 x + 5
18(x + 5) = 15(3x − 3)
18x + 90 = 45x − 45
135 = 27x
x=5
BD = 3x − 3
BD = 3(5) − 3
BD = 12
AB BD
=
by the Triangle Angle Bisector Theorem.
AC CD
Substitute the given values.
Cross Products Property
Distributive Property
Simplify.
Divide.
Substitute for x.
Simplify.
Feedback
A
B
C
D
This is the value of x, now find the value of BD.
This is the value of BC, now find the value of BD.
Correct!
This is the value of CD, now find the value of BD.
PTS:
OBJ:
TOP:
DOK:
1
DIF: Average
REF: 1b8eaede-4683-11df-9c7d-001185f0d2ea
7-4.4 Using the Triangle Angle Bisector Theorem
LOC: MTH.C.11.08.03.04.008
7-4 Applying Properties of Similar Triangles
KEY: triangle angle bisector theorem
DOK 2
1
ID: C
2. ANS: B
It is given that PR Ä NQ, so
PN
2
=
8
5
8(PN) = 10
PN = 1.25
RQ
PN
=
by the Triangle Proportionality Theorem.
QM
NM
Substitute 2 for RQ, 8 for QM, and 5 for NM.
Cross Products Property
Divide by 8.
Feedback
A
B
C
D
Use the Triangle Proportionality Theorem to find the length.
Correct!
Use the Triangle Proportionality Theorem to find the length.
Use the Triangle Proportionality Theorem to find the length.
PTS:
OBJ:
STA:
LOC:
TOP:
DOK:
1
DIF: Average
REF: 1b89ea26-4683-11df-9c7d-001185f0d2ea
7-4.1 Finding the Length of a Segment
NY.NYLES.MTH.05.GEO.G.G.46 | NY.NYLES.MTH.05.GEO.G.G.67
MTH.C.11.01.02.01.001 | MTH.C.11.08.03.04.002
7-4 Applying Properties of Similar Triangles
KEY: similar triangles | segment length
DOK 2
2
ID: C
3. ANS: A
Because the sun’s rays are parallel, we know that ∠J ≅ ∠C .
Therefore ∆ABC ∼ ∆GHJ by AA similarity.
The height of the tree is the length of GH .
AB GH
=
Corresponding sides are proportional.
GJ
AC
40 GH
=
Substitute.
18
16
(40)(18) = 16(GH)
Cross Products Property
45 = GH
Divide both sides by 16.
The height of the tree is 45 feet.
Feedback
A
B
C
D
Correct!
Set up the proportions. Compare height to height and shadow to shadow.
Set up the proportions. Compare height to height and shadow to shadow.
Set up the proportions. Compare height to height and shadow to shadow.
PTS:
OBJ:
LOC:
KEY:
1
DIF: Basic
7-5.1 Application
MTH.C.09.03.006
indirect measurement | similar
REF:
NAT:
TOP:
DOK:
3
1b91384a-4683-11df-9c7d-001185f0d2ea
NT.CCSS.MTH.10.9-12.G.SRT.5
7-5 Using Proportional Relationships
DOK 2
ID: C
SHORT ANSWER
1. ANS:
P = 42 ft, A = 40.5 ft 2
For the two triangles the similarity ratio is
18
12
3
, or 2 .
3
By the Proportional Perimeters and Areas Theorem, the ratio of the triangles’ perimeters is also 2 , and the
Ê 3 ˆ2 9
ratios of their areas is ÁÁÁ 2 ˜˜˜ = 4 .
Ë ¯
Perimeter:
P
3
=
Set up the ratio.
28 2
2(P) = (28)(3)
Cross Products Property
P = 42 feet
Simplify.
Area:
A 9
=
18 4
4(A) = (18)(9)
A = 40.5 feet 2
PTS:
OBJ:
LOC:
KEY:
1
DIF: Average
REF: 1b95fd02-4683-11df-9c7d-001185f0d2ea
7-5.4 Using Ratios to Find Perimeters and Areas
NAT: NT.CCSS.MTH.10.9-12.G.SRT.5
MTH.C.09.01.02.005
TOP: 7-5 Using Proportional Relationships
similarity ratio | proportion | similar triangles | area
DOK: DOK 2
4