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Quadrilateral Properties & Proofs

Total questions: 50

Worksheet time: 2hrs 27mins

Name
Class
Date
1.
A rhombus has all of the properties of a 
a)
Parallelogram
b)

Trapezoid

c)
Kite
d)
Square
2.
Which statement is FALSE? 
A parallelogram _____________
a)
Has 2 sets of parallel sides
b)
Has diagonals that are perpendicular
c)
Has diagonals that bisect each other
3.

ABCD is a rhombus. What is the size of angle AED? 

a)
60 
b)
45
c)
90
d)
180
4.
Which quadrilateral is also considered a rhombus, rectangle, and parallelogram?
a)
Trapezoid
b)
Triangle
c)
Square
d)
Hexagon
5.
Classify the quadrilateral in as many ways as possible.
a)
quadrilateral, parallelogram
b)
rectangle
c)
quadrilateral,parallelogram, rectangle
d)
quadrilateral,parallelogram, rectangle, square
6.

Which statement is always true for parallelograms?

a)

All sides have the same length

b)

All angles have the same measure

c)

Opposite sides are equal in length

d)

Opposite angles have different measures

7.

Which describes a rhombus?

a)

has all right angles

b)

has all acute angles

c)

has all equal sides

d)

has all obtuse angles

8.

Brayden is working on a report in which he will compare and contrast the different types of quadrilaterals. Which statement should NOT be included in his report?

a)

All rhombuses are squares.

b)

All squares are parallelograms.

c)

All squares and rectangles have opposite sides that are congruent.

d)

All parallelograms, rectangles, and squares have opposite angles that are congruent.

9.

Select all shapes where the sum of the angles is 360o

a)
b)
c)
d)
10.

Select all the correct statements:

a)

A rectangle has four right angles

b)

A rectangle has one pair of parallel lines

c)

A rectangle (which is not a square) has four lines of symmetry

d)

A rectangle (which is not a square) has rotational symmetry of order two

11.
Name that shape. 
a)
square
b)
square
rhombus
c)
quadrilateral
parallelogram
rhombus
d)
quadrilateral
parallelogram
square
12.

A rectangle has

a)

Opposite sides are equal

b)

Opposite sides are parallel

c)

Four angles that each measure 90 degrees

d)

All four sides are equal

13.
A rectangle is ______ a square
a)
Sometimes
b)
Always
c)
Never
14.
HIJK is a rectangle. Find the value of length of each diagonal.
HJ = 3x + 5  and IK = 5x - 9 
a)
7
b)
14
c)
26
d)
7/3
15.
Find the measure of angle 2
a)
54
b)
108
c)
72
d)
36
16.
Find the measure of angle 1
a)
54
b)
108
c)
72
d)
36
17.

Find the value of x.

a)

x = 50

b)

x = 40

c)

x = 30

d)

x = 90

18.

Find the value of x.

a)

x = 1

b)

x = 3

c)

x = 2

d)

x = 0

19.

Using the properties of the special parallelogram, solve for x and y.

a)

x = 2, y = 1

b)

x = 2, y = 0

c)

x = 1, y = 1

d)

x = 1, y = 0

20.
If the figure is a rectangle, the value of x is...
a)
2
b)
12
c)
13
d)
28
21.

MNKL is a square. Find the measure of angle MKN.

a)

180 degrees

b)

90 degrees

c)

60 degrees

d)

45 degrees

22.
Consecutive angles of a parallelogram are supplementary
a)
sometimes true
b)
always true
c)
never true
23.
Diagonals of a parallelogram bisect each other
a)
always true
b)
sometimes true
c)
never true
24.
Opposite angles of a square are supplementary
a)
always true 
b)
sometimes true
c)
never true
25.
Which statement about the diagonals of a parallelogram is ALWAYS true?
a)
The diagonals of a parallelogram are congruent.
b)
The diagonals of a parallelogram are perpendicular.
c)
The diagonals of a parallelogram bisect each other.
d)
The diagonals of a parallelogram bisect opposite angles. 
26.
The figure is a parallelogram.  
Solve for x.  
Give a reason.
a)
1
b)
10
c)
4
d)
5
27.
The figure is a parallelogram.  
Solve for x.  
Give a reason.
a)
7
b)
1
c)
5
d)
2
28.
When given a figure is a parallelogram, what can we infer?
a)
Opposite sides are congruent
b)
Opposite sides are parallel
c)
Opposite angles are congruent
d)
All of these
29.
When given a figure is a parallelogram, what can we NOT infer?
a)
Consecutive angles are supplementary
b)
Diagonals bisect each other
c)
Diagonals intersect at right angles.
d)
All sides are congruent
30.

If CT=9, find AT

(a)  

31.

If AT=4x-7 and CT=-x+13, find the value of X

(a)  

32.

Which quadrilateral(s) have diagonals that bisect each other?

a)

Parallelogram

b)

Rectangle

c)

Square

d)

Rhombus

e)

Trapezoid

33.

Which quadrilateral(s) have perpendicular diagonals?

a)

Parallelogram

b)

Rectangle

c)

Square

d)

Rhombus

e)

Trapezoid

34.

Which quadrilateral(s) have diagonals that bisect opposite angles?

a)

Parallelogram

b)

Rectangle

c)

Square

d)

Rhombus

e)

Trapezoid

35.

Which of the following are the angles of a quadrilateral

a)

24, 96, 48, 252

b)

48, 64, 108, 140

c)

32, 55, 66, 108

d)

360, 360, 360, 360

36.
Solve for x in the rectangle.
a)
x=2
b)
x=7
c)
x=8
d)
x=3
37.

What is reason #3? Make sure you write-in the reasons on your proofs.

a)

Definition of a parallelogram

b)

Definition of a quadrilateral

c)

opposite sides are congruent property

d)

opposite sides are supplementary

38.

What is reason #4?

a)

Same-side interior angles theorem

b)

alternate interior angles theorem

c)

consecutive angles theorem

d)

supplementary angles

39.

What is reason #5?

a)

vertical angles theorem

b)

stuck together and sharing a side theorem

c)

shared side property

d)

reflexive property

40.

What is reason #6?

a)

SSS Triangle Congruence Postulate

b)

AAS Triangle Congruence Theorem

c)

ASA Triangle Congruence Theorem

d)

SAS Triangle Congruence Theorem

41.

What is reason #7?

a)

Coffee Please Control the Creamer

b)

PSATs

c)

SATs

d)

CPCTC

42.
What is reason #2?
a)
Vertical angles are congruent.
b)
Consecutive angles are congruent.
c)
Alternate interior angles are congruent.
d)
Definition of Bisect
43.

What is #3 Reason?

a)

Same Line

b)

Perpendicular Lines

c)

Segment Bisector

d)

Reflexive Property

44.

Fill in the Reason #3.

a)

Alternate interior angles are congruent.

b)

Vertical angles are congruent.

c)

Reflexive Property

d)

∥⟶\parallel\longrightarrow alternate interior angles are congruent

45.
What is the "reason" for step 5 of the proof?
a)
Angle Bisector Theorem
b)
Reflexive property
c)
CPCTC Theorem
d)
Proof
46.
What is always the 1st statement in reason column of a proof?
a)
Prove
b)
Given
c)
Reason
d)
Statement
47.

Determine the correct reason for statement #2.

a)

all sides are congruent property

b)

all sides are parallel property

c)

Definition of a quadrilateral

d)

Definition of parallelogram

48.

Determine the correct reason for statement #3.

a)

Alternate Interior Angles Theorem

b)

Alternate Exterior Angles Theorem

c)

Same- Side Angles Theorem

d)

Congruent Angles Theorem

49.

Given: AB and DC are both parallel and congruent. Why would angle ABD be congruent to angle CDB?

a)

vertical angles are congruent.

b)

opposite angles of a parallelogram are congruent.

c)

alternate interior angles are congruent.

d)

corresponding angles are congruent.

50.

Given - AE is congruent to EC and DE is congruent to EB in parallelogram ABCD. Which property does this demonstrate?

a)

opposite sides of a parallelogram are congruent.

b)

the diagonals cut a parallelogram into 2 congruent triangles.

c)

the diagonals of a parallelogram bisect each other.

d)

the diagonals of a parallelogram are perpendicular.

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