Name: ________________________ Class: ___________________ Date: __________
Geometry Chapter 6 Practice Test
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Judging by appearance, classify the figure in as many ways as possible.
a.
b.
c.
d.
____
2. Find the values of the variables and the lengths of the sides of this kite.
a.
b.
____
rectangle, square, quadrilateral, parallelogram, rhombus
rectangle, square, parallelogram
rhombus, trapezoid, quadrilateral, square
square, rectangle, quadrilateral
x = 9, y = 13; 7, 15
x =13, y = 9; 7, 15
c.
d.
3. Which statement is true?
a. All quadrilaterals are rectangles.
b. All quadrilaterals are squares.
c. All rectangles are quadrilaterals.
d. All quadrilaterals are parallelograms.
1
x = 9, y = 13; 11, 20
x =13, y = 9; 11, 11
ID: A
Name: ________________________
____
ID: A
4. Which Venn diagram is NOT correct?
a.
b.
____
d.
5. ABCD is a parallelogram. If m∠CDA = 66, then m∠BCD =
a.
____
c.
66
b.
124
c.
114
?
. The diagram is not to scale.
d.
132
6. LMNO is a parallelogram. If NM = x + 15 and OL = 3x + 5, find the value of x and then find NM and OL.
a.
b.
x = 7, NM = 20, OL = 22
x = 5, NM = 20, OL = 20
c.
d.
2
x = 7, NM = 22, OL = 22
x = 5, NM = 22, OL = 20
Name: ________________________
____
7. Find the values of the variables in the parallelogram. The diagram is not to scale.
a.
b.
____
x = 49, y = 29, z = 102
x = 29, y = 49, z = 131
c.
d.
x = 49, y = 49, z = 131
x = 29, y = 49, z = 102
8. In the figure, the horizontal lines are parallel and AB = BC = CD. Find KL and FG. The diagram is not to
scale.
a.
b.
____
ID: A
KL = 7.6, FG = 7.6
KL = 5.1, FG = 7.6
c.
d.
KL = 5.1, FG = 5.1
KL = 7.6, FG = 5.1
9. Find values of x and y for which ABCD must be a parallelogram. The diagram is not to
scale.
a.
x = 10, y = 38
b.
x = 10, y = 21
c.
3
x = 10, y = 7
d.
x = 7, y = 10
Name: ________________________
ID: A
____ 10. Based on the information in the diagram, can you prove that the figure is a parallelogram? Explain.
a.
b.
c.
d.
Yes; both pairs of opposite sides are congruent.
Yes; opposite angles are congruent.
No; you cannot prove that the quadrilateral is a parallelogram.
Yes; two opposite sides are both parallel and congruent.
____ 11. If ON = 5x − 4, LM = 4x + 7, NM = x − 7, and OL = 2y − 6, find the values of x and y for which LMNO must
be a parallelogram. The diagram is not to scale.
1
5
a.
x = 4, y = 5
c.
x = 11, y =
b.
x = 4, y =
1
5
d.
x = 11, y = 5
____ 12. If m∠B = m∠D = 41, find m∠C so that quadrilateral ABCD is a parallelogram. The diagram is not to scale.
a.
41
b.
139
c.
4
82
d.
278
Name: ________________________
ID: A
____ 13. Which statement can you use to conclude that quadrilateral XYZW is a parallelogram?
a.
b.
XW ≅ YZ and XY ≅ WZ
XW ≅ WZ and XY ≅ WZ
c.
d.
YN = NX and XN = NY
XW ≅ YZ and XY ≅ YZ
____ 14. In the rhombus, m∠1 = 6x, m∠2 = x + y, and m∠3 = 18z. Find the value of each variable. The diagram is
not to scale.
a.
b.
x = 15, y = 165, z = 10
x = 30, y = 75, z = 10
c.
d.
x = 15, y = 75, z = 5
x = 30, y = 165, z = 5
____ 15. DEFG is a rectangle. DF = 5x – 5 and EG = x + 11. Find the value of x and the length of each diagonal.
a. x = 4, DF = 13, EG = 13
c. x = 4, DF = 15, EG = 15
b. x = 4, DF = 15, EG = 18
d. x = 2, DF = 13, EG = 13
____ 16. Which description does NOT guarantee that a quadrilateral is a parallelogram?
a. a quadrilateral with both pairs of opposite sides congruent
b. a quadrilateral with the diagonals bisecting each other
c. a quadrilateral with consecutive angles supplementary
d. quadrilateral with two opposite sides parallel
5
Name: ________________________
ID: A
____ 17. m∠R = 130 and m∠S = 80. Find m∠T. The diagram is not to scale.
a.
65
b.
70
c.
35
d.
80
____ 18. One side of a kite is 8 cm less than four times the length of another side. The perimeter of the kite is 78 cm.
Find the lengths of the sides of the kite.
a. 9.4 cm and 29.6 cm
c. 23.5 cm
b. 23.5 cm and 86 cm
d. 9.4 cm
____ 19. In quadrilateral MNOP, ∠M ≅ ∠N. Which of a parallelogram, trapezoid, or rhombus could quadrilateral
MNOP be?
a. parallelogram or rhombus
c. trapezoid only
b. parallelogram only
d. any of the three
Essay
20. Given: SV ≅ TU and SV Ä TU
Prove: VX = XT
Other
21. Give a convincing argument that quadrilateral ABCD with A(–3, –4), B(0, –2), C(6, –2), and D(3, –4) is a
parallelogram.
6
ID: A
Geometry Chapter 6 Practice Test
Answer Section
MULTIPLE CHOICE
1. ANS:
OBJ:
TOP:
KEY:
2. ANS:
OBJ:
TOP:
3. ANS:
OBJ:
KEY:
4. ANS:
OBJ:
KEY:
5. ANS:
OBJ:
STA:
6. ANS:
OBJ:
STA:
KEY:
7. ANS:
OBJ:
STA:
8. ANS:
OBJ:
STA:
KEY:
9. ANS:
REF:
OBJ:
STA:
KEY:
10. ANS:
REF:
OBJ:
STA:
KEY:
11. ANS:
REF:
OBJ:
STA:
A
PTS: 1
DIF: L2
REF: 6-1 Classifying Quadrilaterals
6-1.1 Classifying Special Quadrilaterals
NAT: NAEP 2005 G3f
6-1 Example 1
special quadrilaterals | quadrilateral | parallelogram | rhombus | square | rectangle | kite | trapezoid
C
PTS: 1
DIF: L2
REF: 6-1 Classifying Quadrilaterals
6-1.1 Classifying Special Quadrilaterals
NAT: NAEP 2005 G3f
6-1 Example 3
KEY: algebra | kite
C
PTS: 1
DIF: L2
REF: 6-1 Classifying Quadrilaterals
6-1.1 Classifying Special Quadrilaterals
NAT: NAEP 2005 G3f
reasoning | kite | parallelogram | quadrilateral | rectangle | rhombus | special quadrilaterals
B
PTS: 1
DIF: L2
REF: 6-1 Classifying Quadrilaterals
6-1.1 Classifying Special Quadrilaterals
NAT: NAEP 2005 G3f
reasoning | quadrilateral | Venn Diagram
NOT: TC 12, MC, Static.
C
PTS: 1
DIF: L2
REF: 6-2 Properties of Parallelograms
6-2.1 Properties: Sides and Angles NAT: NAEP 2005 G3f
PA 2.9.C
TOP: 6-2 Example 1
KEY: parallelogram | consectutive angles
B
PTS: 1
DIF: L2
REF: 6-2 Properties of Parallelograms
6-2.1 Properties: Sides and Angles NAT: NAEP 2005 G3f
PA 2.9.C
TOP: 6-2 Example 2
parallelogram | algebra | Theorem 6-1
D
PTS: 1
DIF: L2
REF: 6-2 Properties of Parallelograms
6-2.1 Properties: Sides and Angles NAT: NAEP 2005 G3f
PA 2.9.C
KEY: parallelogram | opposite angles | consectutive angles | transversal
D
PTS: 1
DIF: L2
REF: 6-2 Properties of Parallelograms
6-2.2 Properties: Diagonals and Transversals
NAT: NAEP 2005 G3f
PA 2.9.C
TOP: 6-2 Example 4
Theorem 6-4 | parallel lines | transversal
C
PTS: 1
DIF: L2
6-3 Proving That a Quadrilateral is a Parallelogram
6-3.1 Is the Quadrilateral a Parallelogram?
NAT: NAEP 2005 G3f
PA 2.9.C
TOP: 6-3 Example 1
algebra | parallelogram | Theorem 6-5 | diagonal
B
PTS: 1
DIF: L2
6-3 Proving That a Quadrilateral is a Parallelogram
6-3.1 Is the Quadrilateral a Parallelogram?
NAT: NAEP 2005 G3f
PA 2.9.C
TOP: 6-3 Example 2
opposite angles | parallelogram | Theorem 6-8
D
PTS: 1
DIF: L2
6-3 Proving That a Quadrilateral is a Parallelogram
6-3.1 Is the Quadrilateral a Parallelogram?
NAT: NAEP 2005 G3f
PA 2.9.C
KEY: algebra | parallelogram | Theorem 6-7 | opposite sides
1
ID: A
12. ANS:
REF:
OBJ:
STA:
13. ANS:
REF:
OBJ:
STA:
14. ANS:
OBJ:
STA:
KEY:
15. ANS:
OBJ:
STA:
KEY:
16. ANS:
OBJ:
STA:
17. ANS:
OBJ:
STA:
18. ANS:
OBJ:
STA:
19. ANS:
OBJ:
STA:
B
PTS: 1
DIF: L2
6-3 Proving That a Quadrilateral is a Parallelogram
6-3.1 Is the Quadrilateral a Parallelogram?
NAT: NAEP 2005 G3f
PA 2.9.C
KEY: opposite angles | parallelogram | Theorem 6-8
A
PTS: 1
DIF: L3
6-3 Proving That a Quadrilateral is a Parallelogram
6-3.1 Is the Quadrilateral a Parallelogram?
NAT: NAEP 2005 G3f
PA 2.9.C
KEY: proof | reasoning | parallelogram
C
PTS: 1
DIF: L2
REF: 6-4 Special Parallelograms
6-4.1 Diagonals of Rhombuses and Rectangles
NAT: NAEP 2005 G3f
PA 2.9.C
TOP: 6-4 Example 1
algebra | diagonal | rhombus | Theorem 6-13
C
PTS: 1
DIF: L2
REF: 6-4 Special Parallelograms
6-4.1 Diagonals of Rhombuses and Rectangles
NAT: NAEP 2005 G3f
PA 2.9.C
TOP: 6-4 Example 2
rectangle | algebra | Theorem 6-11 | diagonal
D
PTS: 1
DIF: L3
REF: 6-4 Special Parallelograms
6-4.2 Is the Parallelogram a Rhombus or a Rectangle?
NAT: NAEP 2005 G3f
PA 2.9.C
KEY: square | reasoning
B
PTS: 1
DIF: L2
REF: 6-5 Trapezoids and Kites
6-5.1 Properties of Trapezoids and Kites
NAT: NAEP 2005 G3f
PA 2.9.C
KEY: kite | sum of interior angles
A
PTS: 1
DIF: L2
REF: 6-5 Trapezoids and Kites
6-5.1 Properties of Trapezoids and Kites
NAT: NAEP 2005 G3f
PA 2.9.C
KEY: kite | algebra | word problem | problem solving
D
PTS: 1
DIF: L3
REF: 6-5 Trapezoids and Kites
6-5.1 Properties of Trapezoids and Kites
NAT: NAEP 2005 G3f
PA 2.9.C
KEY: quadrilateral | rectangle | rhombus | trapezoid | parallelogram | reasoning
ESSAY
20. ANS:
[4] Since SV Ä TU , ∠SVT ≅ ∠UTV and ∠VSU ≅ ∠TUS
by the Alternating Interior Angles Theorem. Thus
[3]
[2]
[1]
ΔSVX ≅ ΔUTX by ASA, and VX = XT by CPCTC.
correct idea, some details inaccurate
correct idea, not well organized
correct idea, one or more significant steps omitted
PTS:
OBJ:
STA:
KEY:
1
DIF: L4
REF: 6-3 Proving That a Quadrilateral is a Parallelogram
6-3.1 Is the Quadrilateral a Parallelogram?
NAT: NAEP 2005 G3f
PA 2.9.C
parallelogram | proof | reasoning | paragraph proof | extended response | rubric-based question
2
ID: A
OTHER
21. ANS:
2
.
3
2
Slope of CD is .
3
Slope of BC is 0.
Slope of AD is 0.
Slope of AB is
AB Ä CD and BC Ä AD.
Therefore ABCD is a parallelogram.
PTS: 1
DIF: L3
REF: 6-3 Proving That a Quadrilateral is a Parallelogram
OBJ: 6-3.1 Is the Quadrilateral a Parallelogram?
NAT: NAEP 2005 G3f
STA: PA 2.9.C
KEY: parallelogram | coordinate plane | algebra | slope | writing in math
3