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THEOREMS ON PARALLELOGRAM

Total questions: 55

Worksheet time: 2hrs 50mins

Name
Class
Date
1.

Find x.

a)

120

b)

100

c)

80

d)

60

2.
a)

trapezoid

b)

kite

c)

rhombus

d)

rectangle

3.

Determine the most specific name for the quadrilateral.

a)

rectangle

b)

rhombus

c)

square

d)

kite

4.

Find x.

a)

3

b)

4

c)

5

d)

6

5.

Classify the quadrilateral (give the most specific name

a)

kite

b)

rectangle

c)

rhombus

d)

trapezoid

6.

Which two quadrilaterals have congruent consecutive angles?

a)

parallelogram and rectangle

b)

rectangle and rhombus

c)

kite and square

d)

square and rectangle

7.

Two consecutive angles of a parallelogram have measures (𝑥+ 20)° and 3x. What is the measure of the smaller angle?

a)

60

b)

120

c)

180

d)

320

8.

How many congruent triangles are formed when a diagonal is drawn in a parallelogram?

a)

1

b)

2

c)

3

d)

4

9.

What is the measure of <LIE?

a)

90

b)

70

c)

50

d)

45

10.

Diagonals of a rhombus bisect each other.

a)

never true

b)

always true

c)

sometimes true

11.

Diagonals of a rhombus bisect each other.

a)

always true

b)

sometimes true

c)

never tue

12.

The sum of the interior angles of a rectangle is 180.

a)

always true

b)

sometimes true

c)

never true

13.

A square is a rhombus.

a)

always true

b)

sometimes true

c)

never true

14.

Diagonals of a square are angle bisectors.

a)

always true

b)

sometimes true

c)

never true

15.

Diagonals of a rhombus are congruent.

a)

always true

b)

sometimes true

c)

never true

16.

Classify the quadrilateral (give the most specific name)

a)

Parallelogram

b)

Square

c)

Rectangle

d)

Rhombus

17.

Classify the quadrilateral (give the most specific name)

a)

Parallelogram

b)

Square

c)

Rectangle

d)

Rhombus

18.

Classify the quadrilateral (give the most specific name)

a)

Parallelogram

b)

Square

c)

Rectangle

d)

Rhombus

19.

Determine the most specific name for the quadrilateral.

a)

Parallelogram

b)

Rectangle

c)

Rhombus

d)

Square

20.

Two properties of a quadrilateral are listed below.

· The quadrilateral always has 4 congruent angles

· The quadrilateral does not always have 4 congruent sides


Which of the following quadrilaterals has both properties?

a)

Parallelogram

b)

Rectangle

c)

Rhombus

d)

Square

21.
ABCD is a rectangle.  m∠BCE = 4x-23 and m∠DCE = 5+5x.  Find m∠BCE. 
a)
25
b)
12
c)
130
d)
32
22.
ABCD is a rectangle.  m∠BCA = 58.  Find m∠BAC. 
a)
90
b)
58
c)
64
d)
32
23.
Find the measure of angle 4
a)
44
b)
68
c)
90
d)
136
24.
Find y.
a)
2
b)
4
c)
15
d)
10
25.
Which of these properties is NOT a property of a rhombus?
a)
Diagonals bisect each other
b)
Diagonals are perpendicular
c)
Diagonals create angle bisectors of each angle
d)
Diagonals are congruent
26.
Which quadrilateral has all the properties listed:
- All sides are congruent
- Opposite sides are parallel
- Opposite angles are congruent
-Sides are not perpendicular 
a)
Square
b)
Rectangle
c)
Trapezoid
d)
Rhombus
27.

What is the value of x in the parallelogram shown?

a)

132

b)

66

c)

114

d)

48

28.

Solve for x given that the figure is a parallelogram.

a)

7

b)

2

c)

0

d)

4

29.

Diagonals of a rhombus bisect each other.

a)

always true

b)

sometimes true

c)

never tue

30.

A square is a rhombus.

a)

always true

b)

sometimes true

c)

never true

31.

Classify the quadrilateral (give the most specific name)

a)

Parallelogram

b)

Square

c)

Rectangle

d)

Rhombus

32.

Classify the quadrilateral (give the most specific name)

a)

Parallelogram

b)

Square

c)

Rectangle

d)

Rhombus

33.

Two properties of a quadrilateral are listed below.

· The quadrilateral always has 4 congruent angles

· The quadrilateral does not always have 4 congruent sides


Which of the following quadrilaterals has both properties?

a)

Parallelogram

b)

Rectangle

c)

Rhombus

d)

Square

34.

ABCD is a rectangle.  m DB‾\overline{DB}   = 58.  Find m∠ AC‾\overline{AC}  . 

a)
90
b)
58
c)
64
d)
32
35.

Find the measure of angle 4 if the figure is a rhombus.

a)
44
b)
68
c)
90
d)
136
36.

What theorem is represented by the figure?

a)

Theorem 1

b)

Theorem 2

c)

Theorem 3

d)

Theorem 4

37.

What theorem best describe this given illustration?

a)

The diagonals of rhombus are perpendicular to each other.

b)

The diagonals of a rhombus are always congruent.

c)

The diagonals of a rhombus bisects the opposite angles.

d)

The diagonals of a rhombus are supplementary.

38.

What do we call a quadrilateral whose opposite sides are parallel and whose diagonal divides it into two congruent triangles?

a)

Trapezoid

b)

Parallelogram

c)

Kite

d)

None of the above

39.
Which is NOT a property of a parallelogram?
a)
Diagonals bisect each other
b)
Diagonals are congruent
c)
Both pairs of opposite sides are parallel
d)
Both pairs of opposite angles are congruent
40.
The diagonals of a parallelogram always ... 
a)
are congruent
b)
are perpendicular
c)
bisect each other
d)
are parallel
41.
The diagonals of a parallelogram always ... 
a)
are congruent
b)
are perpendicular
c)
bisect each other
d)
are parallel
42.
In a parallelogram, opposite angles are ________.
a)
congruent
b)
supplementary
c)
consecutive
d)
parallel
43.
a)
x = 23, y = 10
b)
x = 10, y = 23
44.
If ABCD is a parallelogram, what is the length of BD? 
a)
10
b)
11
c)
7
d)
5
45.
a)
x = 40 , y = 40 
b)
x = 30, y = 30
c)
x = 40, y = 30
d)
x = 30, y = 40
46.
a)
x = 70, y = 80
b)
x = 70, y = 30
c)
x = 80, y = 70
d)
x = 80, y = 30
47.
a)
x = 30, y = 40
b)
x = 40, y = 30
c)
x = 40, y = 15
d)
x = 30, y = 30
48.
The figure is a parallelogram.  
Solve for x.  
a)
12
b)
4
c)
6
d)
2
49.
The figure is a parallelogram.  
Solve for x.  
Give a reason.
a)
2
b)
10
c)
11
d)
12
50.
In parallelogram CARS, m<C = 5x - 20 and m<A = 3x + 40. Find the value of x. 
a)
15
b)
20
c)
30
d)
130
51.
The figure is a parallelogram.  
Solve for x.  
a)
1
b)
11
c)
7
d)
6
52.
a)
x = 9, y = 4
b)
x = 6, y = 4
c)
x = 6, y = 2
d)
x = 4, y = 2
53.
Is this quadrilateral a parallelogram?
a)
Yes. Diagonals bisect each other
b)
no
c)
Yes. Opposite angles are congruent
d)
Yes. Opposite sides are congruent
54.
A rectangle is also a _____________
a)
square
b)
parallelogram
c)
rhombus
d)
it is just a rectangle
55.
The diagonals of a ________ are congruent
a)
Parallelogram
b)
Rectangle and square
c)
Rhombus and square
d)
Trapezoid

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