Extra Review - Chapter 6

(1)

Chapter Test Form A

Circle the best answer.

1. Which term does NOT describe the figure?

A concave C polygon B hexagon D regular

2. What is the sum of the measures of the interior angles of a 5-sided convex polygon?

A 72 C 540 B 360 D 900

3. What is the value of a?

A 60 B 80

4. The diagonals of

.

ABCD intersect at X. Which is NOT true?

A ∠DAB≅∠BCD

B m∠DAB+ m∠CBA= 180°

C BC≅AD

D AX ≅ XB

Use the figure for Exercises 5 and 6.

5. WXYZ is a parallelogram. Which is m∠W?

A 68° B 112°

6. WXYZ is a parallelogram. What is the value of x?

A 7 B 10

7. Which MUST be a parallelogram?

A Figure 1 B Figure 2

8. If EF GH|| , what additional information would allow you to conclude that EFGH is a parallelogram?

A EF ≅GH

B FG≅EH

9. Which is NOT always true? A A square is a rhombus.

B A rectangle is a parallelogram. C A rhombus is a rectangle. D A square is a rectangle.

10. PQRS is a rectangle. PR= 26. What is the value of x?

(2)

Name ________________________________________ Date ___________________ Class __________________

Holt McDougal Geometry

Polygons and Quadrilaterals

Chapter Test

Form B

1. Which best describes the figure?

A regular convex heptagon B irregular convex heptagon C irregular concave heptagon D irregular convex hexagon 2. What is the measure of each interior

angle in a regular convex nonagon? F 40° H 180°

G 140° J 1260° 3. What is the value of a?

A 2 C 180

B 90 D Not here

4. The diagonals of

.

ABCD intersect at X. Which is always true?

F BX XD≅ G AX XB≅ H ∠A ≅ ∠D

J m∠A + m∠C = 180°

5. In

.

DEFG, what is EG?

A 25 C 50

B 30 D Not here

6. In

.

JKLM, what is the value of m∠K?

F 15° H 65° G 57° J 115°

7. QR ST|| . Which additional information is NOT enough to conclude that QRST is a parallelogram?

A RS QT|| C QR ST≅ B RS QT≅ D ∠Q ≅ ∠S 8. Which of the quadrilaterals MUST be

parallelograms?

F A only H Neither A nor B G B only J Both A and B 9. Which is NOT always true?

A The diagonals of a rectangle divide the rectangle into four

nonoverlapping isosceles triangles. B The diagonals of a square divide the

square into four nonoverlapping right triangles.

C The longer diagonal of a rhombus is perpendicular to two sides of the rhombus.

D The sum of the lengths of the diagonals of a rhombus is less than the perimeter of the rhombus.

Name ________________________________________ Date ___________________ Class __________________

Polygons and Quadrilaterals

Chapter Test

Form A continued

11. JKLM is a rhombus. If m∠JML = 70°, what is the value of m∠JKM?

A 35° B 55° C 70° D 110°

12. Given: ABCD is a parallelogram, ⊥

AC BD, and AB CD≅ . Conclusion: ABCD is a square.

What can be said about the conclusion?

A Valid B Not valid

13. Which statement is needed to prove

.

EFGH is a rectangle?

A EG HF⊥ B EG HF≅

A kite

B parallelogram C quadrilateral D trapezoid

15. What is m∠F in the isosceles trapezoid?

A 79° B 101°

16. In trapezoid PQRS, what is the length of midsegment XY?

A 48 cm B 51 cm Chapter

6

108

(3)

Chapter Test

Form B

A regular convex heptagon B irregular convex heptagon C irregular concave heptagon D irregular convex hexagon 2. What is the measure of each interior

angle in a regular convex nonagon? F 40° H 180°

G 140° J 1260° 3. What is the value of a?

A 2 C 180

B 90 D Not here

4. The diagonals of

.

ABCD intersect at X. Which is always true?

F BX XD≅ G AX XB≅ H ∠A ≅ ∠D

J m∠A + m∠C = 180°

5. In

.

DEFG, what is EG?

A 25 C 50

B 30 D Not here

6. In

.

JKLM, what is the value of m∠K?

F 15° H 65° G 57° J 115°

7. QR ST|| . Which additional information is NOT enough to conclude that QRST is a parallelogram?

A RS QT|| C QR ST≅ B RS QT≅ D ∠Q ≅ ∠S 8. Which of the quadrilaterals MUST be

parallelograms?

F A only H Neither A nor B G B only J Both A and B 9. Which is NOT always true?

A The diagonals of a rectangle divide the rectangle into four

nonoverlapping isosceles triangles. B The diagonals of a square divide the

square into four nonoverlapping right triangles.

C The longer diagonal of a rhombus is perpendicular to two sides of the rhombus.

D The sum of the lengths of the diagonals of a rhombus is less than the perimeter of the rhombus.

Chapter Test

Form A continued

11. JKLM is a rhombus. If m∠JML = 70°, what is the value of m∠JKM?

A 35° B 55° C 70° D 110°

12. Given: ABCD is a parallelogram, ⊥

AC BD, and AB CD≅ . Conclusion: ABCD is a square.

What can be said about the conclusion?

A Valid B Not valid

13. Which statement is needed to prove

.

EFGH is a rectangle?

A EG HF⊥ B EG HF≅

A kite

B parallelogram C quadrilateral D trapezoid

15. What is m∠F in the isosceles trapezoid?

A 79° B 101°

16. In trapezoid PQRS, what is the length of midsegment XY?

A 48 cm B 51 cm

(4)

Name ________________________________________ Date ___________________ Class __________________

Polygons and Quadrilaterals

Chapter Test

Form C

1. The perimeter of a regular polygon is 36 centimeters. The length of one side is 4.5 centimeters. Which identifies the

polygon?

A decagon C octagon B hexagon D pentagon

2. The figure is a regular polygon. What is the value of x?

F 30 H 90

G 60 J 120

3. The exterior angles of a triangle measure 5x°, (x + 61)°, and (3x + 38)°. Which is the best classification of the triangle? A acute C obtuse

B equiangular D right

4. Three vertices of parallelogram ABCD are A(−2, −2), B(2, 1), and C(0, 7). What are the coordinates of vertex D?

F (−4, 4) H (0, −8) G (4, 10) J Not here 5. ABCD is a parallelogram. What is the

perimeter of �AED?

A 5.5 C 19

B 29 D 44

6. In

.

ABCD, what is m∠DAB?

F 7° H 110°

G 70° J Not here

7. For what value of x will the quadrilateral be a parallelogram?

A 4 C 6

B 5 D 7

8. If AD BC|| , which CANNOT be used to justify the statement that ABCD is a parallelogram?

F EF ABHJJG⊥ and EF CDHJJG⊥

G m∠BEF + m∠EFC = 180°

H ∠ABD ≅∠CDB J BA DC≅

9. The vertices of a quadrilateral are formed by the intersection of the lines for the equations y = x, y =−x, y = 3, and y =−3. Which term best describes the quadrilateral?

A parallelogram C rhombus B rectangle D square

Name ________________________________________ Date ___________________ Class __________________

Polygons and Quadrilaterals

Chapter Test

Form B continued

10. WXYZ is a rectangle. Which is NOT an expression for WT ?

F 5x + 18 H 10x − 12 G 7x + 6 J 12x − 10 11. Which set of numbers could be the

measures of ∠DAB, ∠ACB, and ∠DBC, respectively?

A 114°, 57°, 32.5° B 115°, 32.5°, 57.5° C 116°, 57.5°, 32.5° D 117°, 58.5°, 31.5°

12. What additional information would allow you to conclude that JKLM is a rhombus?

F JK ML|| and JM KL|| . G JM JK≅

H JL and MK bisect each other. J JL MK≅

13. Which is the best name for the quadrilateral with vertices at (2, 2), (5, −2), (1, −5), and (−2, −1)? A parallelogram C rhombus B rectangle D square

14. In kite UVWX, m∠XUV = 84�, and m∠WVX = 68�. What is m∠VWX?

F 22° H 44° G 42° J 45° 15. GE = 5x + 2 and DF = 8x − 7.

What is GE?

A 16 B 17 C 18 D 19

16. In trapezoid PQRS, if YX is the midsegment, what could be the lengths of PQ and SR?

F 4 cm and 8 cm G 9 cm and 15 cm H 17 cm and 31 cm J 18 m and 30 m Chapter

6

110

(5)

Chapter Test

Form A

1. Write True or False. The figure is a regular polygon.

_________________________________________

2. Find the sum of the measures of the interior angles of the polygon.

_________________________________________

3. Find the measure of each exterior angle of a regular quadrilateral.

_________________________________________

4. Write True or False. If AB CD|| , then ABCD is a parallelogram.

_________________________________________

Use the figure for Exercises 5 and 6.

5. ABCD is a parallelogram. Find the value of x.

_________________________________________

6. ABCD is a parallelogram. Find m∠C.

________________________________________

7. Write True or False. The quadrilateral is a parallelogram.

________________________________________

8. In the figure, JM KL|| . Show that the quadrilateral is a parallelogram for x = 3.

________________________________________

9. Write True or False. A square is a rhombus.

________________________________________

10. ABCD is a rectangle. AD = 15, AC = 25, and DC = 20. Find BD.

________________________________________

(6)

Name ________________________________________ Date ___________________ Class __________________

Polygons and Quadrilaterals

Chapter Test

Form B

1. Name the polygon by its number of sides and tell whether it is regular or irregular.

_________________________________________

2. Find the measures of each interior angle of a regular octagon.

_________________________________________

3. Find the value of a.

_________________________________________

4. Write a biconditional statement to define the term parallelogram.

_________________________________________

5. ABCD is a parallelogram. Find AB and BX.

_________________________________________

6. EFGH is a parallelogram. Find m∠E.

_________________________________________

7. Write True or False. The quadrilateral must be a parallelogram.

________________________________________

8. Show that JKLM is a parallelogram for x = 7 and y = 14.

________________________________________

9. Complete the sentence. A ________ is a parallelogram that has the properties of both a ________ and a ________.

________________________________________

10. ABCD is a rectangle with diagonals BD and AC that intersect at X. BD = 12x − 6 inches and

AX = 4x + 5 inches. Find DX.

________________________________________ Name ________________________________________ Date ___________________ Class __________________

Polygons and Quadrilaterals

Chapter Test

Form A continued

11. RSTU is a rhombus. m∠SRU = 112. Find m∠TRU.

_________________________________________

12. Write True or False. If EF HG|| and ||

EH FG, then

.

EFGH is a rectangle.

_________________________________________

13. Given: UVWX is a parallelogram and

≅ .

UV XU

Conclusion: UVWX is a rhombus. Determine whether the conclusion is valid.

_________________________________________

14. In kite JKLM, m∠JMN = 25°. Find m∠NJM.

________________________________________

15. In trapezoid ABCD, find m∠A.

________________________________________

16. Find the length of the midsegment of trapezoid PQRS.

________________________________________

Chapter

6

114

(7)

Chapter Test

Form B

1. Name the polygon by its number of sides and tell whether it is regular or irregular.

_________________________________________

2. Find the measures of each interior angle of a regular octagon.

_________________________________________

3. Find the value of a.

_________________________________________

4. Write a biconditional statement to define the term parallelogram.

_________________________________________

5. ABCD is a parallelogram. Find AB and BX.

_________________________________________

6. EFGH is a parallelogram. Find m∠E.

_________________________________________

7. Write True or False. The quadrilateral must be a parallelogram.

________________________________________

8. Show that JKLM is a parallelogram for x = 7 and y = 14.

________________________________________

9. Complete the sentence. A ________ is a parallelogram that has the properties of both a ________ and a ________.

________________________________________

10. ABCD is a rectangle with diagonals BD and AC that intersect at X. BD = 12x − 6 inches and

AX = 4x + 5 inches. Find DX.

________________________________________

Chapter Test

Form A continued

11. RSTU is a rhombus. m∠SRU = 112. Find m∠TRU.

_________________________________________

12. Write True or False. If EF HG|| and ||

EH FG, then

.

EFGH is a rectangle.

_________________________________________

13. Given: UVWX is a parallelogram and

≅ .

UV XU

Conclusion: UVWX is a rhombus. Determine whether the conclusion is valid.

_________________________________________

14. In kite JKLM, m∠JMN = 25°. Find m∠NJM.

________________________________________

16. Find the length of the midsegment of trapezoid PQRS.

________________________________________

(8)

Name ________________________________________ Date ___________________ Class __________________

Polygons and Quadrilaterals

Chapter Test

Form C

1. Identify the figure as specifically as possible.

_________________________________________

2. An interior angle of a regular convex polygon measures 144°. How many sides does the polygon have?

_________________________________________

3. The exterior angles of a convex pentagon measure (18x + 12)°, 16x°, (8x+ 6)°, (10x − 12)°, and (5x + 12)°. Determine the measure of the largest interior angle.

_________________________________________

4. Three vertices of parallelogram PQRS are P(−1, 3), Q(4, 1), and R(1, −2). Find the coordinates of vertex S.

_________________________________________

5. Given

.

ABCD determine the value , of y.

_________________________________________

6. In

.

EFGH, the diagonals intersect at Y. If EY = x2_{and GY}₌_2x₊_{3, determine the} length of EG.

_________________________________________

7. Prove that JKLM is a parallelogram.

________________________________________

8. Use the definition of parallelogram to show that the quadrilateral with vertices A(−4, 4), B(−2, 0), C(6, 4), and D(4, 8) is a parallelogram.

________________________________________

9. Give the best name for the quadrilateral with vertices (−2, 1), (−3, −2), (4, −1), and (3, −4).

________________________________________ Name ________________________________________ Date ___________________ Class __________________

Polygons and Quadrilaterals

Chapter Test

Form B continued

11. RSTQ is a rhombus. Find m∠PST.

_________________________________________

12. Given: WXYZ is a parallelogram. WY and XZ bisect each other and

⊥ . WY XZ

Conclusion: WXYZ is a rectangle. Determine whether the conclusion is valid. If not, tell why not.

_________________________________________

13. Tell whether the parallelogram is a rectangle, rhombus, or square.

_________________________________________

14. In kite JKLM, m∠LMN = 25°, and m∠LKN = 43°. Find m∠MLK.

________________________________________

16. XY is the midsegment of trapezoid ABCD. Find AB.

________________________________________

Chapter

6

116

(9)

Section Quiz: Lessons 6-1 Through 6-3

1. D 6. F

2. H 7. B

3. D 8. J

4. H 9. B

5. A

Section Quiz: Lessons 6-4 Through 6-6

1. A 6. G

2. J 7. D

3. A 8. J

4. J 9. A

5. A

Chapter Test Form A: Multiple Choice

1. D 9. C

2. C 10. A

3. A 11. A

4. D 12. B

5. A 13. B

6. A 14. A

7. B 15. A

8. A 16. A

Chapter Test Form B: Multiple Choice

1. C 9. C

2. G 10. J

3. A 11. D

4. F 12. G

5. C 13. D

6. H 14. H

7. B 15. B

8. J 16. H

Chapter Test Form C: Multiple Choice

1. C 9. D

2. G 10. H

3. D 11. B

4. F 12. F

5. D 13. B

6. G 14. J

7. C 15. A

8. J 16. F

Chapter Test Form A: Free Response

1. True 2. 540° 3. 90° 4. False 5. 11 6. 66° 7. True

8. Find JM and KL.

JM = 5x − 1 and KL = 3x + 5 Given JM = 5(3) − 1 = 14 Subst. and simplify. KL = 3(3) + 5 = 14 Subst. and simplify. Since JM = KL and JM KL& , JKLM is a parallelogram by Theorem 6-3-1. 9. True

10. 25 11. 56° 12. True 13. valid 14. 65° 15. 104° 16. 72

Chapter Test Form B: Free Response

1. irregular hexagon 2. 135°

3. 120°

4. A quadrilateral is a parallelogram if and only if it has two pairs of parallel sides. 5. AB = 30; BX = 25

(10)

3. a. BD AC≅ ; If the diagonals of a parallelogram are congruent, then it is a rectangle.

b. AD CD⊥ (or AD AB⊥ ); All sides are congruent and all angles are right angles.

c. yes; All sides of a rhombus are equal in length, so the perimeter is 4(38), or 152.

Cumulative Test

1. D 23. C

2. H 24. H

3. C 25. D

4. F 26. F

5. B 27. D

6. H 28. G

7. D 29. B

8. H 30. H

9. D 31. B

10. F 32. J

11. D 33. D

12. F 34. J

13. D 35. D

14. G 36. G

15. B 37. B

16. J 38. J

17. C 39. B

18. G 40. H

19. B 41. A

20. G 42. H

21. A 43. A

22. G

8. m∠J = (9y + 1)°= [9(14) + 1]°= 127°; m∠L = (10y − 13)°= [10(14) − 13]°

= 127°; m∠K = (7x + 4)°= [7(7) + 4]°

= 53°; Since 127°+ 53°= 180°, ∠K is supplementary to both ∠J and ∠L. JKLM is a parallelogram by Theorem 6-3-4. 9. square; rhombus; rectangle

10. 21 in. 11. 33°

12. Not valid; possible answer: conditions for a rectangle are 1 ∠ of a

.

is a rt.

∠ or the diagonals of a

.

are ≅. While the quadrilateral is a

.

and a rhombus, neither of the conditions for a rectangle are met.

13. Sample answer:

_DF = _{[2 ( 5)] + (1 0)}− − 2 − 2

= ₇2+₁2 = _{50 5 2}=

_EG= _{[1 ( 4)]}− − 2 + − −_{[( 2) 3]}2

= ₅2+ −_{( 5)}2 = _{50 5 2}=

The diagonals are congruent so by Theorem 6-5-2, DEFG is a rectangle.

slope of = − = − −

1 0 1

2 ( 5) 7 DF

slope of = − − = − = − −

2 3 _{5 1}

1 ( 4) 5 EG

⎛ ⎞_{⎜ ⎟} ≠ −

⎝ ⎠1 (1) 1,7 so DF is not perpendicular to EG.

So DEFG is not a rhombus and therefore cannot be a square. DEFG is a rectangle. 14. 112°

15. 104°

16. 48

Chapter Test Form C: Free Response

1. irregular, concave hexagon 2. 10 sides

3. 138°

4. (−4, 0) 5. 5 6. 2 or 18

7. It is given that ∠KJL ≅∠MLJ, so by the Converse of the Alternate Interior Angles Theorem, JK LM& . It is also given that

≅ .

JK LM Since one pair of opposite sides are both ≅ and parallel, JKLM is a parallelogram.

8. slope of = − = = − − − − −

4 0 4 ₂

4 ( 2) 2 AB

slope of = − = = − − −

8 4 4 ₂

4 6 2

CD

slope of = − = = − −

8 4 4 1

4 ( 4) 8 2 AD

slope of = − = = − −

4 0 4 1

6 ( 2) 8 2 BC

Since both pairs of opposite sides are parallel (same slope), ABCD is a parallelogram by definition. 9. rectangle

10. 32 2 11. 6 12. True 13. rectangle 14. kite 15. 8 or −2 16. 3

Performance Assessment

1. a.parallelogram; Both pairs of opposite sides are congruent, and the figure does not appear to be either a rhombus or rectangle.

b. x = 5 c. 60

2. a. kite; Exactly two pairs of adjacent sides are congruent, and all four sides are not congruent.

b. x = 10 c. 26

256