Skills Practice - Mater Academy Charter Middle/ High...represents all types of quadrilaterals with at least one pair of parallel sides. Draw this part of the Venn diagram and label

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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362 Chapter 10 ● Skills Practice

10

12. 13.

14. 15.

Name the type of quadrilateral that best describes each figure. Explain your answer.

16.

17.


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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


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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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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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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


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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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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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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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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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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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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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.




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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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Calculate the number of sides for each polygon.

19. The measure of each angle of a regular polygon is 108º.




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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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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?


that measures 120º?










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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?


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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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110° 110°

70° 70°


126°

104°120°

90° 100°


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112°

75°133°

130° 90°


85°

67°

150° 58°

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78°

94°83°

105°


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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

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y

10

12

14

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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


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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


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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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Classify the quadrilateral. Explain your answer.

11.

x86

D (13, 7)

B (5, 8)

A (14, 12)

C (4, 3)2

4

6

8

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10

12

14

16


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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

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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


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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

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Documents

Skills Practice - Mater Academy Charter Middle/ High...represents all types of quadrilaterals with at least one pair of parallel sides. Draw this part of the Venn diagram and label