Geometry R
Quadrilateral Packet
Due 1/17/17
Name _________________________
MULTIPLE CHOICE
1. Which of the following is NOT a characteristic of all parallelograms?
A) Diagonal bisect each other
B) Opposite angles are congruent
C) Diagonals are angle bisectors
D) Opposite sides are congruent
2. Which of the following is NOT a characteristic of all parallelograms?
A) Opposite angles are supplementary
B) Opposite angles are congruent
C) Opposite sides are parallel
D) Opposite sides are congruent
3. Which of the following is NOT a characteristic of all parallelograms?
A) Consecutive angles are supplementary
B) Opposite angles are congruent
C) Diagonals bisect each other
D) Diagonals are perpendicular
4. Which of the following is a characteristic of all parallelograms?
A) Diagonals are angle bisectors
B) Diagonals are congruent
C) Diagonals bisect each other
D) Diagonals are perpendicular
5. Which of the following is not a special type of parallelogram?
A) Square
B) Rhombus
C) Rectangle
D) Isosceles Trapezoid
6. Which of the following is NOT a characteristic of all rectangles?
A) Consecutive angles are supplementary
B) Opposite angles are congruent
C) Diagonals bisect each other
D) Diagonals are perpendicular
7. Which of the following is a characteristic of all rectangles?
A) Diagonals are angle bisectors
B) Diagonals are congruent
C) Diagonals are parallel
D) Diagonals are perpendicular
8. Which of the following is NOT a characteristic of all rectangles?
A) Four congruent angles
B) Four congruent sides
C) Diagonals bisect are congruent
D) Opposite angles are congruent
9. Which of the following is NOT a characteristic of all rectangles?
A) Diagonals bisect each other
B) Opposite sides are congruent
C) Diagonals are perpendicular
D) Four congruent angles
10. Which of the following is NOT a characteristic of all rhombi?
A) Diagonals bisect each other
B) Opposite sides are congruent
C) Diagonals are perpendicular
D) Four congruent angles
11. Which of the following is NOT a characteristic of all rhombi?
A) Four congruent sides
B) Diagonals are angle bisectors
C) Diagonals are perpendicular
D) Diagonals are congruent
12. Which of the following is NOT a characteristic of all rhombi?
A) Consecutive angles are supplementary
B) Opposite sides are parallel
C) Four congruent angles
D) Diagonals bisect each other
13. Which of the following is NOT a characteristic of all squares?
A) Diagonals are congruent
B) Diagonals are angle bisectors
C) Diagonals intersect at 45°
D) Diagonals form 4 congruent right isosceles ∆’s
14. Which of the following group of quadrilaterals have diagonals that are perpendicular?
A) Rhombus, Square
B) Rhombus, Parallelogram, Square
C) Rectangle, Square
D) Rectangle, Rhombus, Square
15. Which of the following group of quadrilaterals have congruent diagonals?
A) Rhombus, Square
B) Rhombus, Parallelogram, Square
C) Rectangle, Square
D) Rectangle, Rhombus, Square
16. Which is the largest group of quadrilaterals that have consecutive supplementary angles?
A) Rhombus, Square. Rectangle
B) Rhombus, Parallelogram, Square
C) Rectangle, Square, Parallelogram, Rhombus
D) Parallelogram, Square
17. Which of the following group of quadrilaterals have diagonals that are angle bisectors?
A) Rhombus, Square
B) Rhombus, Parallelogram, Square
C) Rectangle, Square
D) Rectangle, Rhombus, Square
18. A rhombus has diagonals of 6 cm and 8 cm, what is the length of its side?
A) 3 cm
B) 4 cm
C) 5 cm
D) 10 cm
TRUE/FALSE
1. A rhombus has four congruent angles.
T or F
2. A rectangle has diagonals that bisect each other.
T or F
3. A square has four congruent sides.
T or F
4. Squares and rectangles are special types of parallelograms.
T or F
5. A kite is a parallelogram
T or F
.
6. Diagonals in a rhombus are angle bisectors and intersect at right angles.
T or F
7. All parallelograms are rectangles.
T or F
8. All rhombi are parallelograms.
T or F
9. If you have 4 congruent angles and 4 congruent sides you must be a square.
T or F
10. Diagonals bisect angles in a parallelogram.
T or F
11. A quadrilateral is a 4 sided polygon.
T or F
12. Consecutive sides are congruent in a rectangle.
T or F
13. If a parallelogram has 4 ≅ angles, then it must be a square.
T or F
14. A square is both a rhombus & a rectangle
T or F
15. All rectangles are parallelograms.
T or F
16. All rhombi are rectangles.
T or F
SHORT ANSWER
1. Circle whether the relationship is (A)lways, (S)ometimes, or (N)ever True.
a) A rhombus is a quadrilateral
b) A rectangle is a rhombus.
c) Adjacent sides of a rectangle are congruent.
d) Diagonals of a square are perpendicular
e) Diagonals of a parallelogram are congruent.
f) If ABCD is a parallelogram, then AB = CD
g) Square is a rectangle
h) A parallelogram is a rhombus
i) A rhombus is a square
2 B
A
1
D
68°
3
A
A
A
A
A
A
A
A
A
2
C
55° 1
A
N
N
N
N
N
N
N
N
N
C
B
C
S
S
S
S
S
S
S
S
S
2
D
1
B
3
A
D
2 a) Given Parallelogram BCAD
b) Given Rhombus ABCD
c) Given Square ABCD
Find m∠1 = _________
Find m∠1 = _________
Find m∠ADC = _______
Find m∠2 = _________
Find m∠2 = _______
Find m∠1 = _______
Find m∠3 = _________
Find m∠3 = _________
Find m∠2 = _______
3. What are the missing measures in Parallelogram SRQP?
m∠9 = 66˚
m∠2 = 14˚
m∠1 = 16˚
Q
3
m∠6 = ________
m∠10 = ________
9
m∠11 = ________
m∠3 = ________
4. Form a quadrilateral through transformations.
1
6
T
10
2
P
5
4
11
8
7
S
R
a) Make a quadrilateral by rotating
RST 180° about U.
b) Make a quadrilateral by rotating
∆RST 180° about V.
S
S
o
U
R
V
x
T
o
U
R
V
x
What type of quadrilateral is formed?
T
What type of quadrilateral is formed?
________________________________
________________________________
What did you see in the shape to conclude the type
of quadrilateral?
What did you see in the shape to conclude the type
of quadrilateral?
5. Solve for the missing information.
a) Parallelogram ABCD
B
BY = 1x + 10 and YD = 3x + 2
C
x = _________
m∠BAD = 83°, m∠BCA = 33°, m∠CAB = __________
Y
A
b) Parallelogram ABCD
D
B
C
m∠BYC = 107°, m∠DBC = 43° , m∠DBA = 80°
m∠BCA = __________
m∠DAB = __________
c) Rectangle NOPQ
m∠QNO = __________
m∠NPQ = __________
m∠QNP = __________
m∠NPO = __________
d) Rectangle NOPQ
x = _____________
A
D
O
N
m∠PNO = 25°
NZ = 3x + 6
Y
QO = 10x – 8
Z
Q
P
N
O
QO = ____________
Z
Q
P
e) Rhombus EFGH
F
m∠XFG = 55°
G
m∠XFE = __________
m∠EHG= __________
m∠FEH = __________
m∠FXG = __________
X
E
H
f) Rhombus EFGH
FX = 3 cm
F
XG = 4 cm
G
X
FG = __________ cm
E
H
g) Square MJKL
J
m∠MJL = __________
m∠KGL = ____________
G
M
6. As shown in the diagram of rectangle ABCD below, diagonals
If
and
, then find the length of
7. In the diagram below of rhombus ABCD, the diagonals
, what is the length of one side of rhombus ABCD?
K
and
L
intersect at E.
.
and
intersect at E. If
and
8. In the diagram below, quadrilateral STAR is a rhombus with diagonals and
E.
,
,
,
,
,
, and
Find SR, RT, and
.
intersecting at
.
PROOFS
1. Given: Parallelogram DEFG, K and H are points on
drawn.
2.
Prove:
such that
and
and
are
2. Given: Rectangle ABCD, AF ≅ BE
Prove: DF ≅ CE
3. Given: Parallelogram FLSH, LG ⊥ FS , HA ⊥ FS
Prove: ∠FLG ≅ ∠SHA