Download ExamView - Polygons and Quadrilaterals Classwork.tst

Name: ________________________ Class: ___________________ Date: __________
ID: A
Polygons & Quadrilaterals Classwork
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. The pentagon in the diagram below is formed by five rays.
What is the degree measure of angle x?
a. 72
b. 96
c.
d.
108
112
____
2. In which polygon does the sum of the measures of the interior angles equal the sum of the measures of the
exterior angles?
a. triangle
c. octagon
b. hexagon
d. quadrilateral
____
3. In the diagram below, parallelogram ABCD has diagonals AC and BD that intersect at point E.
Which expression is not always true?
a. ∠DAE ≅ ∠BCE
b. ∠DEC ≅ ∠BEA
c.
d.
AC ≅ DB
DE ≅ EB
____
4. Which statement is true about every parallelogram?
a. All four sides are congruent.
c. Two pairs of opposite sides are
congruent.
b. The interior angles are all congruent.
d. The diagonals are perpendicular to each
other.
____
5. Lucinda wants to build a square sandbox, but has no way of measuring angles. Explain how she can make
sure that the sandbox is square by only measuring length.
a. Arrange four equal-length sides so the diagonals bisect each other.
b. Arrange four equal-length sides so the diagonals are equal lengths also.
c. Make each diagonal the same length as four equal-length sides.
d. Not possible; Lucinda has to be able to measure a right angle.
____
6. A quadrilateral whose diagonals bisect each other and are perpendicular is a
a. rhombus
c. trapezoid
b. rectangle
d. parallelogram
1
Name: ________________________
ID: A
____
7. Isosceles trapezoid ABCD has diagonals AC and BD . If AC = 5x + 13 and BD = 11x − 5 , what is the value of
x?
a. 28
c. 3
3
1
b. 10
d.
4
2
____
8. An artist designs a rectangular quilt piece with different types of ribbon that go from the corner to the center
of the quilt. The dimensions of the rectangle are AB = 10 inches and AC = 14 inches. Find BX .
a.
b.
____
BX = 7 inches
BX = 10 inches
c.
d.
BX = 5 inches
BX = 14 inches
c.
d.
SU = 5
SU = 3
9. TRSU is a rhombus. Find SU .
a.
b.
SU = 7
SU = 1
____ 10. In the diagram below of trapezoid RSUT, RS Ä TU , X is the midpoint of RT , and V is the midpoint of SU .
If RS = 30 and XV = 44, what is the length of TU ?
a. 37
c. 74
b. 58
d. 118
____ 11. In parallelogram STUV, SV = x + 3, VU = 2x − 1, and TU = 4x − 3. What is the length of SV ?
a. 5
c. 7
b. 2
d. 4
Short Answer
12. Find, in degrees, the measures of both an interior angle and an exterior angle of a regular pentagon.
Interior Angle = ________________
Exterior Angle = _______________
2
ID: A
Polygons & Quadrilaterals Classwork
Answer Section
MULTIPLE CHOICE
1. ANS: C
. The sum of the interior angles of a pentagon is (5 − 2)180 = 540.
PTS: 2
REF: 011023ge
STA: G.G.36
TOP: Interior and Exterior Angles of Polygons
2. ANS: D
sum of interior ∠s = sum of exterior ∠s
ÊÁ
(n − 2)180 ˆ˜˜˜
Á
(n − 2)180 = n ÁÁÁ 180 −
˜˜
Á
˜
n
Ë
¯
180n − 360 = 180n − 180n + 360
180n = 720
n=4
3.
4.
5.
6.
7.
PTS: 2
REF: 081016ge
STA: G.G.36
TOP: Interior and Exterior Angles of Polygons
ANS: C
PTS: 2
REF: 061111ge
STA: G.G.38
TOP: Parallelograms
ANS: C
PTS: 2
REF: 011104ge
STA: G.G.38
TOP: Parallelograms
ANS: B
PTS: 2
DIF: L3
REF: 6-4 Special Parallelograms
OBJ: 6-4.2 Is the Parallelogram a Rhombus or a Rectangle?
NAT: NAEP 2005 G3f
STA: NY G.G.39 | NY G.G.41
TOP: 6-4 Example 3
KEY: square | reasoning | Theorem 6-10 | Theorem 6-11 | word problem | problem solving
ANS: A
PTS: 2
REF: 080918ge
STA: G.G.41
TOP: Special Quadrilaterals
ANS: C
The diagonals of an isosceles trapezoid are congruent. 5x + 3 = 11x − 5.
6x = 18
x=3
PTS: 2
REF: fall0801ge
STA: G.G.40
1
TOP: Trapezoids
ID: A
8. ANS: A
AC = BD = 14
1
2
BX = BD
1
BX = 2 (14) = 7
The diagonals of a rectangle are congruent.
A rectangle is a parallelogram. The diagonals of a parallelogram bisect
each other.
Substitute and simplify.
Feedback
A
B
C
D
Correct!
The diagonals of a rectangle are congruent.
The diagonals of a rectangle are congruent.
The diagonals of a rectangle bisect each other.
PTS: 1
NAT: 12.3.3.f
9. ANS: A
TR = RS
5x + 2 = 2x + 5
3x = 3
x=1
US = TR
US = 5x + 2
US = 5(1) + 2
US = 7
DIF: Basic
STA: G.G.39
REF: Page 408
OBJ: 6-4.1 Application
TOP: 6-4 Properties of Special Parallelograms
Definition of a rhombus
Substitute the given values.
Subtract 2x and 2 from both sides.
Divide both sides by 3.
Definition of a rhombus
Substitute 5x + 2 for TR.
Substitute 1 for x.
Simplify.
Feedback
A
B
C
D
Correct!
This is the value of x, not the length of segment SU.
A rhombus has four congruent sides.
A rhombus has four congruent sides.
PTS:
OBJ:
STA:
10. ANS:
1
DIF: Basic
REF: Page 409
6-4.2 Using Properties of Rhombuses to Find Measures
NAT: 12.3.3.f
G.G.39
TOP: 6-4 Properties of Special Parallelograms
B
The length of the midsegment of a trapezoid is the average of the lengths of its bases.
x + 30
= 44.
2
x + 30 = 88
x = 58
PTS: 2
REF: 011001ge
STA: G.G.40
2
TOP: Trapezoids
ID: A
11. ANS: A
Opposite sides of a parallelogram are congruent. 4x − 3 = x + 3. SV = (2) + 3 = 5.
3x = 6
x=2
PTS: 2
REF: 011013ge
STA: G.G.38
SHORT ANSWER
12. ANS:
(5 − 2)180 = 540.
540
= 108 interior. 180 − 108 = 72 exterior
5
PTS: 2
REF: 011131ge
STA: G.G.37
TOP: Interior and Exterior Angles of Polygons
3
TOP: Parallelograms