skills practice - mater academy charter middle/ high...represents all types of quadrilaterals with...
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Chapter 10 ● Skills Practice 361
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Skills Practice Skills Practice for Lesson 10.1
Name _____________________________________________ Date _________________________
Quilting and TessellationsIntroduction to Quadrilaterals
Vocabulary
Write the term that best completes each statement.
1. A quadrilateral with all congruent sides and all right angles is called a(n) .
2. A(n) is a parallelogram whose four sides have the same length.
3. A(n) uses circles to show how elements among sets of numbers or objects
are related.
4. A polygon that has four sides is a(n) .
5. A quadrilateral with two pairs of parallel sides is called a(n) .
6. A(n) of a plane is a collection of polygons that are arranged so that they
cover the plane with no gaps.
7. A(n) is a quadrilateral with exactly one pair of parallel sides.
8. A parallelogram with four right angles is a(n) .
9. A(n) is a four-sided figure with two pairs of adjacent sides of equal length,
with opposite sides not equal in length.
Problem Set
Identify all of the terms from the following list that apply to each figure: quadrilateral, parallelogram, rectangle, square, trapezoid, rhombus, kite.
10. 11.
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12. 13.
14. 15.
Name the type of quadrilateral that best describes each figure. Explain your answer.
16.
17.
Chapter 10 ● Skills Practice 363
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18.
19.
20.
21.
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List all possible names for each quadrilateral based on its vertices.
22. A B
C D
23. E F
H G
24. I
J
K L
25. M
N O
P
Name the indicated parts of each quadrilateral.
26. Name the parallel sides. 27. Name the congruent sides.
A
B
D
C
E F
H
G
Chapter 10 ● Skills Practice 365
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28. Name the congruent angles. 29. Name the right angles.
I J
KL
M N
P O
Draw the part of the Venn diagram that is described.
30. Suppose that part of a Venn diagram has two circles. One circle represents all types
of quadrilaterals with four congruent sides. The other circle represents all types of
quadrilaterals with four congruent angles. Draw this part of the Venn diagram and label
it with the appropriate types of quadrilaterals.
31. Suppose that part of a Venn diagram has two circles. One circle represents all types of
quadrilaterals with two pairs of congruent sides (adjacent or opposite). The other circle
represents all types of quadrilaterals with at least one pair of parallel sides. Draw this part
of the Venn diagram and label it with the appropriate types of quadrilaterals.
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32. Suppose that part of a Venn diagram has two circles. One circle represents all types
of quadrilaterals with two pairs of parallel sides. The other circle represents all types of
quadrilaterals with four congruent sides. Draw this part of the Venn diagram and label it
with the appropriate types of quadrilaterals.
33. Suppose that part of a Venn diagram has two circles. One circle represents all types of
quadrilaterals with four right angles. The other circle represents all types of quadrilaterals
with two pairs of parallel sides. Draw this part of the Venn diagram and label it with the
appropriate types of quadrilaterals.
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Skills Practice Skills Practice for Lesson 10.2
Name _____________________________________________ Date _________________________
When Trapezoids Are Kites Kites and Trapezoids
Vocabulary
Identify all instances of the given term in the figure.
A B
C D
1. isosceles trapezoid
2. base of a trapezoid
3. base angles of a trapezoid
4. diagonal
Problem Set
Use the given figure to answer each question.
5. The figure shown is a kite with �DAB � �DCB. Which sides of the kite are congruent?
A
B
D C
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6. The figure shown is a kite with ___
FG � ___
FE . Which of the kite’s angles are congruent?
E
F
G H
7. Given that IJLK is a kite, what kind of triangles are formed by diagonal __
IL ?
I J
K
L
8. Given that LMNO is a kite, what is the relationship between the triangles formed by diagonal ____
MO ?
M
N
O
L
9. Given that PQRS is a kite, which angles are congruent?
P
Q
R S
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Name _____________________________________________ Date _________________________
10
10. Given that TUVW is a kite, which angles are congruent?
T
U
W V
Write a paragraph proof to prove each statement.
11. Given that ABEF and BCDE are both kites, prove that �FAB � �DCB.
A C
B
F E D
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12. Given that GHKL and IHKJ are both kites, prove that �LGH � �JIH.
G H I
K
L J
13. Given that ABFG and CBED are both kites, prove that � ABG � �EBD.
A C
BG D
F E
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14. Given that HIMN and JILK are both kites, prove that �NHI � �KJI.
H J
IN K
M L
Use the given figure to answer each question.
15. The figure shown is an isosceles trapezoid with ___
AB || ___
CD . Which sides are congruent?
A B
C D
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16. The figure shown is an isosceles trapezoid with ___
EH � ___
FG . Which sides are parallel?
E F
H G
17. The figure shown is an isosceles trapezoid with __
IJ � ___
KL . What are the bases?
I
J
K
L
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18. The figure shown is an isosceles trapezoid with ____
MP � ___
NO . What are the pairs of base
angles?
P
M
NO
19. Given that QRVS is an isosceles trapezoid, which angles are congruent?
Q R
S T U V
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20. Given that WXZY is an isosceles trapezoid, which angles are congruent?
W X
U
Y Z
Write a paragraph proof to prove each statement.
21. Given that ABCD is an isosceles trapezoid, prove that � ACD � �DBC.
A B
D C
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22. Given that EFHG is an isosceles trapezoid, prove that �GEH � �HFG.
E F
G H
23. Given that ABCF and FEDC are isosceles trapezoids, prove that �AFC � �EFC.
A B
F C
E D
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24. Given that GHKL and JKHI are isosceles trapezoids, prove that �HGL � �KJI.
G L
H K
I J
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Skills Practice Skills Practice for Lesson 10.3
Name _____________________________________________ Date _________________________
Binocular Stand DesignParallelograms and Rhombi
Vocabulary
Match each definition to its corresponding term.
1. two angles of a quadrilateral that do not share a. opposite sides
a common side
2. two angles of a quadrilateral that share a common side b. consecutive sides
3. two sides of a quadrilateral that do not intersect c. consecutive angles
4. two sides of a quadrilateral that share a common vertex d. opposite angles
Problem Set
Identify the indicated parts of the given parallelogram.
5. Name the pairs of consecutive sides of the parallelogram.
A B
C D
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6. Name the pairs of opposite sides of the parallelogram.
E F
H G
7. Name the pairs of opposite angles of the parallelogram.
I J
L K
8. Name the pairs of consecutive angles of the parallelogram.
M N
O P
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10
Write a paragraph proof to prove each statement.
9. Given that ___
AB || ___
CD and ___
AC || ___
BD , use the ASA Congruence Theorem to prove that
�B � �C.
A B
C D
10. Given that HG || EF and HE || GF, use the ASA Congruence Theorem to prove that
___
HG � ___
EF .
H E
G F
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11. Given that __
IK || ___
LJ and __
IJ � ___
KL , use the AAS Congruence Theorem to prove that
�IMK � �LMJ.
I J
M
K L
12. Given that NO || QP and ___
NO � ___
QP , use the AAS Congruence Theorem to prove that
�NOM � �QPM.
N O
M
P Q
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10
Use what you know about rhombi to answer each question.
13. What is the relationship between consecutive angles of a rhombus?
14. What is the relationship between opposite angles of a rhombus?
15. What is the relationship between consecutive sides of a rhombus?
16. Explain the difference between parallelograms and rhombi in terms of opposite and
consecutive sides.
Use the given information to complete each two-column proof.
17. If ___
AC bisects �DAB and �DCB, then �D � �B.
A B
D C
Statement Reason
1. 1. Given
2. �DAC � �BAC 2. Defi nition of
3. �DCA � �BCA 3. Defi nition of
4. 4. Refl exive Property of Congruence
5. � ADC � � ABC 5.
6. 6. Defi nition of congruence
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18. If ___
EG bisects �FEH and �FGH, then ___
EF � ___
EH .
E H
F G
Statement Reason
1. ___
EG bisects �FEH and �FGH. 1.
2. �FEG � 2. Defi nition of angle bisector
3. �FGE � 3. Defi nition of angle bisector
4. ___
EG � ___
EG 4.
5. �FEG � 5. ASA Congruence Theorem
6. ___
EF � ___
EH 6. Defi nition of
19. If
__
IK bisects �JIL and __
IL � __
IJ , then �IMJ � �IML.
I L
M
J K
Statement Reason
1. 1. Given
2. �LIM � 2. Defi nition of angle bisector
3. ___
IM � ___
IM 3.
4. 4. Given
5. �JIM � �LIM 5.
6. �IMJ � �IML 6. Defi nition of
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Name _____________________________________________ Date _________________________
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20. If ___
ON bisects �MOP and ____
MO � ___
PO , then ____
MQ � ___
PQ .
M N
Q
O P
Statement Reason
1. ____
ON bisects �MOP. 1.
2. � �POQ 2. Defi nition of angle bisector
3. ____
OQ � ____
OQ 3.
4. 4. Given
5. �MOQ � �POQ 5.
6. 6. Defi nition of congruence
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Skills Practice Skills Practice for Lesson 10.4
Name _____________________________________________ Date _________________________
Positive ReinforcementRectangles and Squares
Vocabulary
Identify similarities and differences between the terms.
1. square and rectangle
Problem Set
Explain why each statement is true.
2. A rectangle is always a parallelogram.
3. A parallelogram is sometimes a rectangle.
4. A rectangle is sometimes a square.
5. A square is always a rectangle.
6. The diagonals of a square are perpendicular.
7. The diagonals of a rectangle are sometimes perpendicular.
8. A rectangle is sometimes a rhombus.
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9. A square is always a rhombus.
10. A rhombus is sometimes a rectangle.
11. A rhombus is sometimes a square.
Given the lengths of the sides of a rectangle, calculate the length of each diagonal. Simplify radicals, but do not evaluate.
12. A rectangular construction scaffold with diagonal support beams is 8 feet high and 10 feet
wide. What is the length of each diagonal? A B
8 ft
C 10 ft D
13. A fence has rectangular sections that are each 4 feet tall and 8 feet long. Each section has a
diagonal support beam. What is the length of each diagonal? E F
4 ft
H 8 ft G
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14. A community garden has a rectangular frame for sugar snap peas. The frame is 9 feet high
and 6 feet wide, and it has two diagonals to strengthen it. What is the length of each
diagonal? M
9 ft
N 6 ft
P
O
15. The sides of a shelving unit are metal rectangles with two diagonals for support. Each
rectangle is 12 inches wide and 40 inches high. What is the length of each diagonal?
12 in
I
J
H
K
40 in
Given the length of a side of a rectangle and the length of a diagonal, calculate the length of another side. Simplify radicals, but do not evaluate.
16. Given that ABDC is a rectangle, calculate CD. A B
10 cm5 cm
C D
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17. Given that EFGH is a rectangle, calculate FG. E H
14 cm6 cm
F G
18. Given that IJKL is a rectangle, calculate IL. I L
16 in.10 in.
J K
19. Given that MNOP is a rectangle, calculate MN. M P
25 in.
N 21 in. O
20. Given that QRTS is a rectangle, calculate QS. Q R
24 ft?
S 22 ft T
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21. Given that UVWX is a rectangle, calculate XW. U V
11 m3 m
X W
22. Given that ABCD is a rectangle, calculate AD. A B
D 12 mm C
12√2 mm
23. Given that EFGH is a rectangle, calculate HG. E H
F 15 m G
15√2 m
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Determine the missing measure. Round decimals to the nearest tenth.
24. A square garden is divided into quarters by diagonal paths. If each diagonal is 50 meters
long, how long is each side of the garden? A B
? 50 m
D C
25. A square porch has diagonal support beams underneath it. If each diagonal beam is 12 feet
long, what is the length of each side of the porch? E F
? 12 ft
H G
26. A heavy picture frame in the shape of a square has a diagonal support across the back. If
each side of the frame is 24 inches, what is the length of the diagonal? I J
?
L 24 in. K
27. A square shelving unit has diagonal supports across the back. If each side of the frame is
60 inches, what is the length of each diagonal? M O
?
N 60 in. P
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Skills Practice Skills Practice for Lesson 10.5
Name _____________________________________________ Date _________________________
Stained GlassSum of the Interior Angle Measures of a Polygon
Vocabulary
Write the term from the box that best completes each statement.
concave polygon interior angle regular polygon
convex polygon reflex angle irregular polygon
1. A(n) is a polygon whose sides all have the same length and
whose angles all have the same measure.
2. Any polygon that contains a reflex angle is a(n) .
3. Any angle whose measure is greater than 180º but less than 360º is a(n) .
4. A(n) is a polygon in which no segments can be drawn to connect
any two vertices so that the segment is outside the polygon.
5. A(n) is any polygon having sides of different lengths and angles of
different measures.
6. An angle that faces the inside of a polygon or shape and is formed by consecutive sides of
the polygon or shape is a(n) .
Problem Set
Use the triangles formed by diagonals to calculate the sum of the interior angle measures of each polygon.
7. Draw all of the diagonals that connect to vertex A. What is the sum of the interior angles of
square ABCD?
A B
D C
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8. Draw all of the diagonals that connect to vertex E. What is the sum of the interior angles of
figure EFGHI?
E
F I
G H
9. Draw all of the diagonals that connect to vertex J. What is the sum of the interior angles of
figure JKMONL?
J K
L M
N O
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10. Draw all of the diagonals that connect to vertex P. What is the sum of the interior angles of
the figure PQRSTUV?
P
Q V
R U
S T
Calculate the sum of the interior angle measures of each convex polygon.
11. A convex polygon has 8 sides.
12. A convex polygon has 9 sides.
13. A convex polygon has 13 sides.
14. A convex polygon has 16 sides.
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For each regular polygon, calculate the measure of each of its interior angles.
15.
16.
17.
18.
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10
Calculate the number of sides for each polygon.
19. The measure of each angle of a regular polygon is 108º.
20. The measure of each angle of a regular polygon is 156º.
21. The measure of each angle of a regular polygon is 160º.
22. The measure of each angle of a regular polygon is 162º.
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Determine whether each polygon is convex or concave.
23.
24.
25.
26.
Determine whether each polygon is regular or irregular.
27.
29.
28.
30.
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Skills Practice Skills Practice for Lesson 10.6
Name _____________________________________________ Date _________________________
PinwheelsSum of the Exterior Angle Measures in a Polygon
Vocabulary
Define each term in your own words.
1. exterior angle
2. regular polygon
Problem Set
Extend each vertex of the polygon to create one exterior angle at each vertex.
3. 4.
5. 6.
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Given the measure of an interior angle of a polygon, calculate the measure of the adjacent exterior angle.
7. What is the measure of an exterior angle if it is adjacent to an interior angle of a polygon
that measures 90º?
8. What is the measure of an exterior angle if it is adjacent to an interior angle of a polygon
that measures 120º?
9. What is the measure of an exterior angle if it is adjacent to an interior angle of a polygon
that measures 108º?
10. What is the measure of an exterior angle if it is adjacent to an interior angle of a polygon
that measures 135º?
11. What is the measure of an exterior angle if it is adjacent to an interior angle of a polygon
that measures 115º?
12. What is the measure of an exterior angle if it is adjacent to an interior angle of a polygon
that measures 124º?
Chapter 10 ● Skills Practice 399
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10
Given the regular polygon, calculate the measure of each of its external angles.
13. What is the measure of each external angle of a square?
14. What is the measure of each external angle of a regular pentagon?
15. What is the measure of each external angle of a regular hexagon?
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16. What is the measure of each external angle of a regular octagon?
Given the regular polygon, calculate the sum of the measures of its external angles.
17. What is the sum of the external angle measures of a regular pentagon?
18. What is the sum of the external angle measures of a regular hexagon?
19. What is the sum of the external angle measures of a regular octagon?
Chapter 10 ● Skills Practice 401
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20. What is the sum of the external angle measures of a square?
Given the diagram of the polygon, calculate the sum of the measures of its external angles.
21. What is the sum of the external angle measures of the polygon?
120°
60° 60°
120°
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22. What is the sum of the external angle measures of the polygon?
110° 110°
70° 70°
23. What is the sum of the external angle measures of the polygon?
126°
104°120°
90° 100°
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24. What is the sum of the external angle measures of the polygon?
112°
75°133°
130° 90°
25. What is the sum of the external angle measures of the polygon?
85°
67°
150° 58°
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26. What is the sum of the external angle measures of the polygon?
78°
94°83°
105°
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Skills Practice Skills Practice for Lesson 10.7
Name _____________________________________________ Date _________________________
Planning a SubdivisionRectangles and Parallelograms in the Coordinate Plane
Vocabulary
Draw a diagram to illustrate each term. Explain your diagram.
1. rectangle
2. parallelogram
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Problem Set
Determine whether any of the sides of the figure are congruent. If so, identify them.
3.
x86
A (3, 9)
B (9, 12)
C (12, 6)
D (6, 3)2
4
6
8
10 12 14 1642
y
10
12
14
16
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4.
x86
H (2, 7)
E (6, 13)
F (10, 7)
G (6, 1)
2
4
6
8
10 12 14 1642
y
10
12
14
16
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5.
x86
D (11, 8)
A (14, 11)
B (15, 8)
C (13, 2)2
4
6
8
10 12 14 1642
y
10
12
14
16
Chapter 10 ● Skills Practice 409
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6.
x86
H (4, 1)
E (2, 9)F (7, 10)
G (10, 4)
2
4
6
8
10 12 14 1642
y
10
12
14
16
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Determine whether any sides of the figure are perpendicular or parallel. If so, identify them.
7.
x86
B (3, 8)
A (7, 10)
D (10, 7)
C (4, 4)
2
4
6
8
10 12 14 1642
y
10
12
14
16
8.
x86
H (10, 7)
E (5, 12)
F (10, 15)
G (13, 12)
2
4
6
8
10 12 14 1642
y
10
12
14
16
Chapter 10 ● Skills Practice 411
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Name _____________________________________________ Date _________________________
10
9.
x86
D (9, 1)
A (5, 4)
B (11, 12)
C (15, 9)
2
4
6
8
10 12 14 1642
y
10
12
14
16
10.
x86
H (6, 11)
E (1, 7)
F (5, 2)
G (10, 6)
2
4
6
8
10 12 14 1642
y
10
12
14
16
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412 Chapter 10 ● Skills Practice
10
Classify the quadrilateral. Explain your answer.
11.
x86
D (13, 7)
B (5, 8)
A (14, 12)
C (4, 3)2
4
6
8
10 12 14 1642
y
10
12
14
16
Chapter 10 ● Skills Practice 413
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Name _____________________________________________ Date _________________________
10
12.
x86
H (13, 6)
E (10, 14)
F (6, 10)
G (9, 2)2
4
6
8
10 12 14 1642
y
10
12
14
16
© 2
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414 Chapter 10 ● Skills Practice
10
13.
x86
B (13, 8)
D (2, 11)
A (9, 15)
C (6, 4)
2
4
6
8
10 12 14 1642
y
10
12
14
16
Chapter 10 ● Skills Practice 415
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Name _____________________________________________ Date _________________________
10
14.
x86
H (12, 11)
E (5, 12)
F(4, 5)
G (11, 4)
2
4
6
8
10 12 14 1642
y
10
12
14
16