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Unit Triangle and Parallelogram Theorems

Total questions: 48

Worksheet time: 3hrs 52mins

Name
Class
Date
1.
Do the following side lengths form a triangle?
2 inches, 2 inches, 4 inches
a)
Yes
b)
No
2.
List the side measures in order, shortest to longest.
a)
QM, QP, MP
b)
MQ, MP, QP
c)
MP, MQ, QP
3.
Identify the smallest angle.
a)
∠A
b)
∠B
c)
∠C
4.

Two sides of a triangle have the following measures. Find the range of possible measure for the third side.
8,128,12  

a)

4<x<164<x<16  

b)

5<x<205<x<20  

c)

4<x<174<x<17  

d)

4<x<204<x<20  

5.

Which of the following is true about the conditional statement below?

If a man is 7 feet tall, then he plays basketball.

a)

Hypothesis: a man is 7 feet tall

Conclusion: he plays basketball

b)

Hypothesis: IF a man is 7 feet tall

Conclusion: THEN he plays basketball

c)

Hypothesis: THEN he plays basketball

Conclusion: IF a man is 7 feet tall

d)

Hypothesis: he plays basketball

Conclusion: a man is 7 feet tall

6.

Which of the following is the CONVERSE of the statement below?

If an object is a bird, then it can fly.

a)

If an object can fly, then it is a bird.

b)

If an object is not a bird, then it cannot fly

c)

If an object cannot fly, then it is not a bird

d)

There is no converse of the statement

7.

Which of the following is the INVERSE of the statement below?

If an object is a computer, then it

has a hard drive.

a)

If an object is not a computer, then it does not have a hard drive.

b)

If an object does not have a hard drive, then it is not a computer.

c)

If an object has a hard drive, then it is a computer.

d)

There is no inverse of the statement.

8.

Which of the following is the CONTRAPOSITIVE of the statement below?

If a species walks on two feet, then

it is human.

a)

If a species is not human, then it does not walk on two feet.

b)

If a species is human, then it walks on two feet.

c)

If a species does not walk on two feet, then it is not human.

d)

There is no contrapositive of the statement.

9.

Which of the following is the BICONDITIONAL of the statement below?

If there is lightning, then there is thunder.

a)

If there is not lightning, then there is not thunder.

b)

If there is thunder, then there is lightning.

c)

There is lightning if and only if (iff) there is thunder.

d)

There is no biconditional statement.

10.
In a parallelogram, opposite angles are ________.
a)
congruent
b)
supplementary
c)
consecutive
d)
parallel
11.
If ABCD is a parallelogram, what is the length of BD? 
a)
10
b)
11
c)
7
d)
5
12.
a)
x = 40 , y = 40 
b)
x = 30, y = 30
c)
x = 40, y = 30
d)
x = 30, y = 40
13.

Which is NOT a property of a parallelogram?

a)

opposite sides are parallel

b)

opposite angles are congruent

c)

diagonals bisect each other

d)

all sides are congruent

14.

If one diagonal of a rectangle is 9 in, what is the measure of the other diagonal

a)

4.5 in

b)

10 in

c)

9 in

d)

6 in

15.
In parallelogram ABCD, what is the measure of ∠DCB?
a)
84
b)
59
c)
96
d)
37
16.
  ABCD is a rectangle.  AB = 14, BC = 9, AC = 22.  Find BD.
a)
11
b)
14
c)
9
d)
22
17.
The figure is a parallelogram.  
Solve for x.  
a)
7
b)
2
c)
0
d)
4
18.
In a rhombus, opposite angles are __________.
a)
congruent
b)
supplementary
c)
corresponding
d)
parallel
19.
Which of the following are NOT true about diagonals of a rhombus?
a)
they are perpendicular
b)
they bisect each other
c)
they are congruent
20.
The figure is a rhombus.  
Solve for x.  
a)
1
b)
11
c)
7
d)
6
21.
If 2 of the angles of a triangle are 30 and 70 degrees, the third angle measures...
a)
80
b)
100
c)
60
d)
90
22.
What is the measure of angle A in the triangle?
a)
116*
b)
25*
c)
62*
d)
54*
23.
Solve for x.
a)
8
b)
-10
c)
-7
d)
6
24.

What is the point of concurrency for the medians of a triangle?

a)

Centroid

b)

Circumcenter

c)

Orthocenter

d)

Incenter

25.

What is the point of concurrency for the perpendicular bisectors of a triangle?

a)

Orthocenter

b)

Incenter

c)

Circumcenter

d)

Excenter

26.

What is the centroid of a triangle?

a)

the point where the medians of the triangle intersect

b)

the point where the angle bisectors of the triangle intersect.

c)

the point where the altitudes of the triangle intersect

d)

the point where the perpendicular bisectors of the triangle intersect

27.

What is the circumcenter of a triangle?

a)

The circumcenter is the point of concurrency of the altitudes of the triangle

b)

The circumcenter of a triangle is the point of concurrency of the perpendicular bisectors of the sides of the triangle.

c)

The circumcenter is the point of concurrency of the medians of the triangle

d)

The circumcenter is the centroid of the triangle

28.
Point O is the circumcenter of the triangle. Find OB
a)
OB = 4
b)
OB = 6
c)
OB = 5.1
d)
Not enough information
29.
Find the value of x
a)
x=28
b)
x=14
c)
x=23
d)
x=46
30.
D is the circumcenter, find DG
a)
15
b)
16
c)
17
d)
19
31.
Find the length of PO.
a)
32
b)
35
c)
26
d)
29
32.
Use the Perp Bisector Theorem to find PQ
a)
10
b)
3
c)
-2
d)
5
33.

X is the centroid of the triangle. If CW = 30, find CX.

a)

20

b)

10

c)

30

d)

15

34.

X is the centroid of the triangle. If BX = 8, find BY.

a)

4

b)

8

c)

12

d)

16

35.

X is the centroid of the triangle. If AZ = 24, find AX.

a)

4

b)

8

c)

12

d)

16

36.
a)

9

b)

4

c)

8

d)

11

37.

AL = 27

Find AP

a)

27

b)

18

c)

9

d)

3

38.

CP = 16

Find CL

a)

24

b)

16

c)

12

d)

8

39.
CF, BE, and AD are the medians of the triangle. If BF =10, find AF.
a)
20
b)
10
c)
5
d)
Not Enough Information
40.
The figure is a parallelogram.  
Solve for x.  
a)
7
b)
2
c)
0
d)
4
41.

Find the measure of the angle indicated in the following parallelogram.

a)

105

b)

36

c)

45

d)

135

42.

What is the length of the missing side?

a)

x = 4

b)

x = 8

c)

x = 10

d)

x = 16

43.

Find the length of the missing side:

a)

14

b)

31

c)

12

d)

13

44.
Translations, reflections and rotations are all known as ________________________.
a)
Geometry
b)
Transformations
c)
Congruent
45.

Rotation Rules (clockwise):

90o rotation: (x, y)→(y, -x)

What are the coordinates for A' after a 90⁰ rotation clockwise?

a)

(1, 3)

b)

(3, 1)

c)

(3, -1)

d)

(1, -3)

46.
Identify the rule after a 90° counter clockwise rotation:
(x, y) ---> ___________
a)
( y, -x)
b)
( -y, x)
c)
( -x, -y)
d)
( y, -x)
47.
State the coordinate of the image of the given point B (-10,-6) under a dilation with center at the origin with the given scale factor k = 1/2.
a)
(5,3)
b)
(20,12)
c)
(-20,-12)
d)
(-5,-3)
48.
Choose the correct scale factor:
a)
2
b)
3
c)
1/3
d)
1/2

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