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REVIEW
Numeric Response
1. In parallelogram LMNO,
, and
. What is the perimeter of parallelogram LMNO?
2. Find the value of x in the rhombus.
2
(-4 x + 15)
2
(8 x + 24x )
Matching
Match each vocabulary term with its definition.
a. base of a trapezoid
b. base angle of a trapezoid
c. rectangle
d. rhombus
e. trapezoid
f. midsegment of a trapezoid
g. leg of a trapezoid
h. isosceles trapezoid
____
1. a quadrilateral with exactly one pair of parallel sides
____
2. the segment whose endpoints are the midpoints of the legs of the trapezoid
____
3. one of the two nonparallel sides of the trapezoid
____
4. one of the two parallel sides of the trapezoid
____
5. one of a pair of consecutive angles whose common side is a base of the trapezoid
Match each vocabulary term with its definition.
a. kite
b. trapezoid
c. rectangle
d. polygon
e. square
f. rhombus
g. parallelogram
____
6. a quadrilateral with four right angles
____
7. a quadrilateral with four congruent sides and four right angles
____
8. a quadrilateral with four congruent sides
____
9. a quadrilateral with two pairs of parallel sides
____ 10. a quadrilateral with exactly two pairs of congruent consecutive sides
Short Answer
1. Find the measure of each interior angle of a regular nonagon.
2. Find the measure of each exterior angle of a regular octagon.
3. Polygon ABCDEFGHIJKL is a regular dodecagon (12-sided polygon). Sides
they meet at point O in the exterior of the polygon. Find m
.
4.
and
are extended so that
. Determine if the quadrilateral must be a parallelogram. Justify your answer.
M
L
K
and
N
5. Show that quadrilateral DEFG is a parallelogram.
y
E (3,
. 10)
10
D (-5,7)
5
F(8, 4)
G (0,1)
–5
5
x
Complete the explanation.
and
have the same slope, so [1]. Since DE = FG, [2]. Because [3], DEFG is a parallelogram.
6. 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
inches and
inches. Find
.
B
C
X
A
D
7. In kite PQRS, m
and m
. Find m
.
Q
O
P
R
S
8. The perimeter of isosceles trapezoid WXYZ is 55.9.
WX, XY, and ZY.
Y
X
19.35
A
B
Z
9.
W
and
R
Q
is the midsegment of WXYZ. If
. Find the value of x so that QRST is isosceles.
>>
>>
S
T
, find ZW,
REVIEW
Answer Section
NUMERIC RESPONSE
1. ANS: 37.8
PTS:
TOP:
DOK:
2. ANS:
1
DIF: Average
6-2 Properties of Parallelograms
DOK 2
0.5
REF: 1b533af2-4683-11df-9c7d-001185f0d2ea
KEY: parallelogram | opposite sides
PTS: 1
DIF: Advanced
REF: 1b55763e-4683-11df-9c7d-001185f0d2ea
TOP: 6-4 Properties of Special Parallelograms
KEY: rhombus | side length
DOK: DOK 2
MATCHING
1. ANS:
REF:
TOP:
2. ANS:
REF:
TOP:
3. ANS:
REF:
TOP:
4. ANS:
REF:
TOP:
5. ANS:
REF:
TOP:
E
PTS: 1
DIF:
1b61620a-4683-11df-9c7d-001185f0d2ea
6-6 Properties of Kites and Trapezoids
F
PTS: 1
DIF:
1b61891a-4683-11df-9c7d-001185f0d2ea
6-6 Properties of Kites and Trapezoids
G
PTS: 1
DIF:
1b63c466-4683-11df-9c7d-001185f0d2ea
6-6 Properties of Kites and Trapezoids
A
PTS: 1
DIF:
1b6626c2-4683-11df-9c7d-001185f0d2ea
6-6 Properties of Kites and Trapezoids
B
PTS: 1
DIF:
1b68891e-4683-11df-9c7d-001185f0d2ea
6-6 Properties of Kites and Trapezoids
Basic
6. ANS:
REF:
TOP:
7. ANS:
REF:
TOP:
8. ANS:
REF:
TOP:
9. ANS:
REF:
DOK:
10. ANS:
REF:
C
PTS: 1
DIF:
1b68b02e-4683-11df-9c7d-001185f0d2ea
6-4 Properties of Special Parallelograms
E
PTS: 1
DIF:
1b6aeb7a-4683-11df-9c7d-001185f0d2ea
6-4 Properties of Special Parallelograms
F
PTS: 1
DIF:
1b6d4dd6-4683-11df-9c7d-001185f0d2ea
6-4 Properties of Special Parallelograms
G
PTS: 1
DIF:
1b6d74e6-4683-11df-9c7d-001185f0d2ea
DOK 1
A
PTS: 1
DIF:
1b6fb032-4683-11df-9c7d-001185f0d2ea
Basic
DOK: DOK 1
Basic
DOK: DOK 1
Basic
DOK: DOK 1
Basic
DOK: DOK 1
Basic
DOK: DOK 1
DOK: DOK 1
Basic
DOK: DOK 1
Basic
DOK: DOK 1
Basic
TOP: 6-2 Properties of Parallelograms
Basic
TOP: 6-6 Properties of Kites and Trapezoids
DOK: DOK 1
SHORT ANSWER
1. ANS:
140
Step 1 Find the sum of the interior angle measures.
(n – 2)180°
Polygon Angle Sum Theorem
= (9 – 2)180°
A nonagon has 9 sides, so substitute 9 for n.
= 1260
Simplify.
Step 2 Find the measure of one interior angle.
The interior angles are , so divide by 9.
= 140
PTS: 1
DIF: Average
REF: 1b2a8bc6-4683-11df-9c7d-001185f0d2ea
OBJ: 6-1.3 Finding Interior Angle Measures and Sums in Polygons
TOP: 6-1 Properties and Attributes of Polygons
KEY: polygon angle sum theorem
DOK: DOK 1
2. ANS:
45°
An octagon has 8 sides and 8 vertices.
sum of exterior angle measures = 360°
Polygon Exterior Angle Sum Theorem
A regular octagon has 8 congruent exterior
measure of one exterior angle =
°
angles, so divide the sum by 8.
The measure of each exterior angle of a regular octagon is 45°.
PTS: 1
DIF: Average
REF: 1b2ab2d6-4683-11df-9c7d-001185f0d2ea
OBJ: 6-1.4 Finding Exterior Angle Measures in Polygons
TOP: 6-1 Properties and Attributes of Polygons
KEY: exterior angle | regular polygon
DOK: DOK 1
3. ANS:
m
= 120
Sketch the relevant sides of the polygon with extended sides meeting at O.
O
G
F
By the Sum of the Exterior Angles of a Polygon Theorem, the sum of the measures of the exterior angles of
the dodecagon is 360°. So, each exterior angle is
. Hence, m
.
By the Triangle Sum Theorem,
which means
.
. So,
,
PTS: 1
DIF: Advanced
REF: 1b2f507e-4683-11df-9c7d-001185f0d2ea
TOP: 6-1 Properties and Attributes of Polygons
KEY: exterior angle | regular polygon
DOK: DOK 2
4. ANS:
No. Only one set of angles and sides are given as congruent. The conditions for a parallelogram are not met.
One set of opposite sides are congruent and one set of opposite angles are congruent. This is insufficient
information to prove that the quadrilateral is a parallelogram.
PTS:
OBJ:
STA:
KEY:
5. ANS:
1
DIF: Average
REF: 1b38d9ee-4683-11df-9c7d-001185f0d2ea
6-3.2 Applying Conditions for Parallelograms
NAT: NT.CCSS.MTH.10.9-12.G.CO.11
MACC.912.G-CO.3.11
TOP: 6-3 Conditions for Parallelograms
conditions for parallelogram
DOK: DOK 2
[1]
[2]
[3] One pair of opposite sides is parallel and congruent.
Find the slopes and lengths of one pair of opposite sides.
and
have the same slope, so
. Since DE = FG,
sides is both congruent and parallel, DEFG is a parallelogram.
. Because one pair of opposite
PTS: 1
DIF: Average
REF: 1b3900fe-4683-11df-9c7d-001185f0d2ea
OBJ: 6-3.3 Proving Parallelograms in the Coordinate Plane
TOP: 6-3 Conditions for Parallelograms
KEY: conditions for parallelogram | coordinate geometry
DOK: DOK 2
6. ANS:
= 7 inches
The diagonals of a rectangle are congruent.
A rectangle is a parallelogram. The diagonals of a parallelogram bisect
each other.
Substitute and simplify.
PTS: 1
DIF: Basic
REF: 1b3dc5b6-4683-11df-9c7d-001185f0d2ea
OBJ: 6-4.1 Application
TOP: 6-4 Properties of Special Parallelograms
KEY: special parallelograms | rectangle | congruent diagonals
DOK: DOK 1
7. ANS:
m
=
Since diagonals of a kite are perpendicular, the four triangles are right triangles.
Diagonals of a kite are
perpendicular.
The acute angles of a right
triangle are complementary.
Substitute the given values.
Subtract.
Theorem: If a quadrilateral is a kite, then exactly one pair of
opposite angles are congruent.
Angle Addition Postulate
Substitute the given values and simplify.
PTS: 1
DIF: Basic
REF: 1b4becce-4683-11df-9c7d-001185f0d2ea
OBJ: 6-6.2 Using Properties of Kites
TOP: 6-6 Properties of Kites and Trapezoids
KEY: kite
DOK: DOK 2
8. ANS:
ZW = 12.9, WX = 8.6, XY = 25.8, and ZY = 8.6
Trapezoid Midsegment Theorem
Simplify.
Solve for ZW.
Isosceles trapezoids have congruent legs.
Perimeter of the trapezoid
Substitute for XY and ZW.
Substitute for ZY.
Simplify.
Solve.
ZW = 12.9, WX = 8.6, XY = 25.8, and ZY = 8.6.
PTS: 1
DIF: Advanced
REF: 1b5313e2-4683-11df-9c7d-001185f0d2ea
TOP: 6-6 Properties of Kites and Trapezoids
KEY: trapezoid midsegment | isosceles trapezoid
DOK: DOK 2
9. ANS:
x = 2.8
Theorem: A trapezoid is isosceles if and only if its diagonals are
congruent.
Definition of congruent segments
Substitute the given values.
Subtract 3x from both sides and add 10 to both sides.
Divide both sides by 5.
PTS:
OBJ:
TOP:
DOK:
1
DIF: Average
REF: 1b4e763a-4683-11df-9c7d-001185f0d2ea
6-6.4 Applying Conditions for Isosceles Trapezoids
6-6 Properties of Kites and Trapezoids
KEY: isosceles trapezoid
DOK 1