chapter 7 practice test #1 - m2 mathdavidbeckeyeipbcc.weebly.com/uploads/5/2/6/3/...chapter 7...
Post on 28-Feb-2021
17 Views
Preview:
TRANSCRIPT
Chapter 7 Practice Test #1
Class Name : M29 Geometry - 2019-20 Term 2 Instructor Name : Mr. Beckey
Student Name : _____________________ Instructor Note :
1. Draw the image of the following segment after a dilation centered at the origin with a scale factor of .
2. A dilation centered at the origin with a scale factor of is applied to
23
3
xx
2 4 6 8 10 12 14 16 18
yy
2
4
6
8
10
12
14
16
18
© 2019 M cGr aw - H i l l Educat i on. Al l R i ghts R eser ved.C hapter 7 Pr ac t i ce T es t #1 Page 1 / 19
2. A dilation centered at the origin with a scale factor of is applied to .
The result is , as shown below.
(a) The arrows below show that the coordinates on the left are mapped to the coordinates on the right. Fill in theblanks to give the coordinates after the dilation.
original coordinates final coordinates
_____, _____
_____, _____
_____, _____
(b) Choose the general rule below that describes the dilation mapping to .
3. For the figure below, do a dilation centered at the origin with a scale factor of
3 XYZ
X 'Y 'Z '
→X , −1 4 → X 'Y , 3 2 → Y '
Z , −3 −1 → Z '
XYZ X 'Y 'Z '
, x y → , 3y 3x , x y → , 3x y
, x y → , x 3y , x y → , 13 x
13 y
, x y → , 13 y
13 x , x y → ,
13 x 3y
, x y → , 3x 3y , x y → , 3x13 y
3
xx
-2-4-6-8-10-12 2 4 6 8 10 12
yy
-2
-4
-6
-8
-10
-12
2
4
6
8
10
12
X
Y
Z
X '
Y '
Z '
© 2019 M cGr aw - H i l l Educat i on. Al l R i ghts R eser ved.C hapter 7 Pr ac t i ce T es t #1 Page 2 / 19
3. For the figure below, do a dilation centered at the origin with a scale factor of .
Then, give the endpoints for both the original figure and the final figure.
Endpoints of original figure:
Left: ____ ____ Right: ____ ____
Endpoints of final figure:
Left: ____ ____ Right: ____ ____
4. Which pairs of figures are congruent? Which pairs are similar?
3
Dilation
, ,
, ,
xx
2 4 6 8 10 12 14 16 18 20
yy
2
4
6
8
10
12
14
16
18
20
0
© 2019 M cGr aw - H i l l Educat i on. Al l R i ghts R eser ved.C hapter 7 Pr ac t i ce T es t #1 Page 3 / 19
4. Which pairs of figures are congruent? Which pairs are similar?
5. The quadrilaterals and are similar.
Find the length of .
6. The table below gives the dimensions of a sculpture and a scale model of the sculpture.
Congruent? Yes No Congruent? Yes No
Similar? Yes No Similar? Yes No
Congruent? Yes No Congruent? Yes No
Similar? Yes No Similar? Yes No
JKLM PQRS
x SP
L
2
4
3
7K J
MR
2.8
5.6
x
9.8Q P
S
© 2019 M cGr aw - H i l l Educat i on. Al l R i ghts R eser ved.C hapter 7 Pr ac t i ce T es t #1 Page 4 / 19
6. The table below gives the dimensions of a sculpture and a scale model of the sculpture.
Find the scale factor of the model to the real sculpture. Write your answer as a fraction in simplest form.
Sculpture Model
Length (inches)
Width (inches)
Height (inches)
7.
(The triangles are not drawn to scale.)
8. The two triangles below are similar.
49 7
35 5
56 8
A
B
C D
E
F
45 ?
63 7
5 8
and are similar. Find the missing side length.ΔABC ΔDEF
© 2019 M cGr aw - H i l l Educat i on. Al l R i ghts R eser ved.C hapter 7 Pr ac t i ce T es t #1 Page 5 / 19
8. The two triangles below are similar.
Also, and as shown below.
Find , , and .
Assume the triangles are accurately drawn.
____
____
____
9. In a scale model of a table, centimeter represents inches.
=m∠ F 60 ° =m∠ E 95 °m∠ J m∠ K m∠ L
m∠ J = °m∠ K = °m∠ L = °
1 9
G
FE
60° 95°
K
J
L
© 2019 M cGr aw - H i l l Educat i on. Al l R i ghts R eser ved.C hapter 7 Pr ac t i ce T es t #1 Page 6 / 19
9. In a scale model of a table, centimeter represents inches.
Scale
Answer the following.
(a) The height of the real table is inches. What is the height ofthe table in the scale model?
____ centimeters
(b) In the scale model, the length of the table is centimeters.What is the length of the real table?
____ inches
10. Find the length .
11. A pole that is tall casts a shadow that is long. At the same time, a nearby building casts a
shadow that is long. How tall is the building? Round your answer to the nearest meter.
12. Decide whether the triangles are similar. If they are, write a similarity statement and state the reason justifying
1 9
:1 cm 9 in
18
4
x
3.3 m 1.08 m48.25 m
2
x
3
7.5
© 2019 M cGr aw - H i l l Educat i on. Al l R i ghts R eser ved.C hapter 7 Pr ac t i ce T es t #1 Page 7 / 19
12. Decide whether the triangles are similar. If they are, write a similarity statement and state the reason justifyingthe similarity.
If necessary, you may learn what the markings on a figure indicate.
Not similar or not necessarily similar
Similar: ___, by the
Angle-Angle (AA) Similarity Property Side-Side-Side (SSS) Similarity Property
Side-Angle-Side (SAS) Similarity Property
Not similar or not necessarily similar
Similar: ___, by the
Angle-Angle (AA) Similarity Property Side-Side-Side (SSS) Similarity Property
Side-Angle-Side (SAS) Similarity Property
Not similar or not necessarily similar
Similar: ___, by the
Angle-Angle (AA) Similarity Property Side-Side-Side (SSS) Similarity Property
Side-Angle-Side (SAS) Similarity Property
13. Use the given information to prove that .
Given:
Prove:
14. In the figure below, and are perpendicular.
STU ~
JKL ~
ABC ~
ABC ~ ADE
=AC
AE
AB
AD
ABC ~ ADE
JL LN
10
4
20
8
T
P
S
Q
U
R
50°30°
J
G
K
I
L
H
9 312
4
15
5
A
F
B
E
CD
A
B
C
D
E
© 2019 M cGr aw - H i l l Educat i on. Al l R i ghts R eser ved.C hapter 7 Pr ac t i ce T es t #1 Page 8 / 19
Complete the following.
xx
yy
O
J
K L M
N
© 2019 M cGr aw - H i l l Educat i on. Al l R i ghts R eser ved.C hapter 7 Pr ac t i ce T es t #1 Page 9 / 19
15. In the figure below, points and are the midpoints of the
(a) Find the slope of and the slope of .JL LN
slope of :JLKL
JK−JK
KL
JK
KL−KL
JK
slope of :LN −MN
LM
LM
MN−LM
MN
MN
LM
(b) It can be shown that .
Based on this, choose the ratio that is equal to .
JKL ~ LMNJK
KL
LM
MN
LN
MN
LM
LN
MN
LM
(c) Using the results above, choose the correct statement below.
slope of slope of JL = − LN
slope of slope of JL = LN
slope of slope of JL · LN = 1
slope of slope of JL · LN = − 1
(d) The result in part (c) is an example of the following rule for any two non-vertical perpendicular lines.
The slopes of the two lines are opposites.
The slopes of the two lines are the same.
The slopes of the two lines are negative reciprocals.
The slopes of the two lines are reciprocals.
© 2019 M cGr aw - H i l l Educat i on. Al l R i ghts R eser ved.C hapter 7 Pr ac t i ce T es t #1 Page 10 / 19
15. In the figure below, points , , and are the midpoints of the sides of .
Suppose , , and .Find the following lengths.
_____
_____
_____
16. In , . Given that , , and , find .
17. Use the given information to complete the proof of the following theorem.
J K L XYZ
=XZ 26 =KL 44 =YZ 78
=JK
=XY
=JY
PQR PQ ST =RP 28 =PQ 49 =ST 28 RS
XY
Z
J
KL
R
T
P Q
S
© 2019 M cGr aw - H i l l Educat i on. Al l R i ghts R eser ved.C hapter 7 Pr ac t i ce T es t #1 Page 11 / 19
17. Use the given information to complete the proof of the following theorem.
If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sidesproportionally.
Given:
Prove:
18. Find the value of each variable.
DC GF
=DG
GE
CF
FE
Statement Reason
1 DC GF Given
2 =~∠EDC ∠EGF _______________
3 =~∠E ∠ Reflexive Property
4 ~CDE FGE _______________
5 =DE
GE FECorr. sides of similar triangles are proportional 4
6 =DE +DG GE _______________
7 =CE +CF FE _______________
8 =+DG GE
GE
+FE
Substitution Property (Using 3 lines) 5 6 7
9 =+DG
GE
GE
GE+
CF
FE
FE
FEFraction Algebra 8
10 =+DG
GE1 +
CF
FE1 Fraction Algebra 9
11 =DG
GE FE_______________
Line(s) Used
F G
E
C D
© 2019 M cGr aw - H i l l Educat i on. Al l R i ghts R eser ved.C hapter 7 Pr ac t i ce T es t #1 Page 12 / 19
18. Find the value of each variable.Simplify your answers as much as possible.
_____
_____
=x
=y
4x
23
4
8
9
y
© 2019 M cGr aw - H i l l Educat i on. Al l R i ghts R eser ved.C hapter 7 Pr ac t i ce T es t #1 Page 13 / 19
Chapter 7 Practice Test #1 Answers for class M29 Geometry -2019-20 Term 2
1.
2.
(a) The arrows below show that the coordinates on the left are mappedto the coordinates on the right. Fill in the blanks to give thecoordinates after the dilation.
original coordinates final coordinates
(b) Choose the general rule below that describes the dilation mapping to .
3.
→X , −1 4 → X ' , −3 12Y , 3 2 → Y ' , 9 6
Z , −3 −1 → Z ' , −9 −3
XYZ X 'Y 'Z '
, x y → , 3y 3x , x y → , 3x y
, x y → , x 3y , x y → , 13 x
13 y
, x y → , 13 y
13 x , x y → ,
13 x 3y
, x y → , 3x 3y , x y → , 3x13 y
xx
2 4 6 8 10 12 14 16 18
yy
2
4
6
8
10
12
14
16
18
© 2019 M cGr aw - H i l l Educat i on. Al l R i ghts R eser ved.C hapter 7 Pr ac t i ce T es t #1 Page 14 / 19
3.
Endpoints of original figure:
Left: Right:
Endpoints of final figure:
Left: Right:
4.
Dilation
, 1 5 , 4 4
, 3 15 , 12 12
xx
2 4 6 8 10 12 14 16 18 20
yy
2
4
6
8
10
12
14
16
18
20
0
© 2019 M cGr aw - H i l l Educat i on. Al l R i ghts R eser ved.C hapter 7 Pr ac t i ce T es t #1 Page 15 / 19
4.
5.
6. Scale factor:
7.
8.
9.
Congruent? Yes No Congruent? Yes No
Similar? Yes No Similar? Yes No
Congruent? Yes No Congruent? Yes No
Similar? Yes No Similar? Yes No
=x 4.2
17
72
m∠ J =60 °m∠ K =25 °m∠ L =95 °
© 2019 M cGr aw - H i l l Educat i on. Al l R i ghts R eser ved.C hapter 7 Pr ac t i ce T es t #1 Page 16 / 19
9.
(a) The height of the real table is inches. What is the height ofthe table in the scale model?
centimeters
(b) In the scale model, the length of the table is centimeters.What is the length of the real table?
inches
10.
11.
12. Not similar or not necessarily similar
Similar: , by the
Angle-Angle (AA) Similarity Property Side-Side-Side (SSS) Similarity Property
Side-Angle-Side (SAS) Similarity Property
Not similar or not necessarily similar
Similar: ___, by the
Angle-Angle (AA) Similarity Property Side-Side-Side (SSS) Similarity Property
Side-Angle-Side (SAS) Similarity Property
Not similar or not necessarily similar
Similar: , by the
Angle-Angle (AA) Similarity Property Side-Side-Side (SSS) Similarity Property
Side-Angle-Side (SAS) Similarity Property
13.
18
2
4
36
5
147 m
STU ~ QPR
JKL ~
ABC ~ FED
10
4
20
8
T
P
S
Q
U
R
50°30°
J
G
K
I
L
H
9 312
4
15
5
A
F
B
E
CD
© 2019 M cGr aw - H i l l Educat i on. Al l R i ghts R eser ved.C hapter 7 Pr ac t i ce T es t #1 Page 17 / 19
13.
14.
15.
Statement Reason Line(s) Used
1 =A C
A E
A B
A DGiven
2 =~∠ A ∠ A Reflexive Property
3 ~A B C A D E SAS Similarity Property 1 2
(a) Find the slope of and the slope of .JL LN
slope of :JLKL
JK−JK
KL
JK
KL−KL
JK
slope of :LN −MN
LM
LM
MN−LM
MN
MN
LM
(b) It can be shown that .
Based on this, choose the ratio that is equal to .
JKL ~ LMNJK
KL
LM
MN
LN
MN
LM
LN
MN
LM
(c) Using the results above, choose the correct statement below.
slope of slope of JL = − LN
slope of slope of JL = LN
slope of slope of JL · LN = 1
slope of slope of JL · LN = − 1
(d) The result in part (c) is an example of the following rule for any two non-vertical perpendicular lines.
The slopes of the two lines are opposites.
The slopes of the two lines are the same.
The slopes of the two lines are negative reciprocals.
The slopes of the two lines are reciprocals.
© 2019 M cGr aw - H i l l Educat i on. Al l R i ghts R eser ved.C hapter 7 Pr ac t i ce T es t #1 Page 18 / 19
15.
16.
17.
18.
=JK 39
=XY 88
=JY 44
=RS 16
Statement Reason
1 DC GF Given
2 =~∠EDC ∠EGF If lines , then corr. s ∠ =~ 1
3 =~∠E ∠E Reflexive Property
4 ~CDE FGE AA Similarity Property 2 3
5 =DE
GE
CE
FECorr. sides of similar triangles are proportional 4
6 =DE +DG GE Segment Addition Property
7 =CE +CF FE Segment Addition Property
8 =+DG GE
GE
+CF FE
FESubstitution Property (Using 3 lines) 5 6 7
9 =+DG
GE
GE
GE+
CF
FE
FE
FEFraction Algebra 8
10 =+DG
GE1 +
CF
FE1 Fraction Algebra 9
11 =DG
GE
CF
FEAddition and Subtraction Properties 10
Line(s) Used
=x 6=y 3
© 2019 M cGr aw - H i l l Educat i on. Al l R i ghts R eser ved.C hapter 7 Pr ac t i ce T es t #1 Page 19 / 19
top related