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GEOM Mid Year Review Ch 1 to Ch 6 _PEARSON

Total questions: 100

Worksheet time: 8hrs 18mins

Name
Class
Date
1.
If m∠XOZ = 74°, find m∠XOY.
a)

37°

b)

74°

c)

90°

d)

148°

2.
Which of the following statements correctly describes perpendicular lines?
a)
Coplanar but do not intersect
b)
Coplanar and intersect at 90 degree angle
c)
Coplanar and intersect at either obtuse or acute angles
d)
Not coplanar
3.
Name a line skew to FG
a)
EH
b)
DC
c)
AD
d)
FB
4.

Which illustration shows the correct construction of an angle bisector?

a)
b)
c)
d)
5.
What is this construction?
a)
Perpendicular Bisector
b)
Perpendicular Through Point Not On Line
c)
Parallel Line Though Given Point
d)
Perpendicular Line Through Point On Line
6.

Which geometric principle is used to justify the construction?

a)

A line perpendicular to one of two parallel lines is perpendicular to the other.

b)

Two lines are perpendicular if they intersect to form congruent adjacent angles.

c)

When two lines are intersected by a transversal and alternate interior angles are congruent, the lines are parallel.

d)

When two lines are intersected by a transversal and the corresponding angles are congruent, the lines are parallel.

7.
Tell whether the angles are complementary or supplementary. Then find the value of x.
a)
Complementary; x=25
b)
Complementary; x=5
c)
Supplementary; x=25
d)
Supplementary; x=5
8.
Find the value of x.
a)
14
b)
60
c)
35
d)
180
9.
Find the length of DE 
a)
12
b)
11
c)
10
d)
13
10.

Your little brother has chocolate sauce on his face. You conclude he must have eaten chocolate sauce.

a)

inductive

b)

deductive

11.
Given, "If I have a Siberian Husky, then I have a dog." Identify the contrapositive.
a)
If I do not have a Siberian Husky, then I do not have a dog.
b)
If I have a dog, then I have a Siberian Husky.
c)
If I do not have a dog, then I do not have a Siberian Husky.
d)
If I do not have a Siberian Husky, then I have a dog. 
12.
What has to happen in order to write a biconditional statement?
a)
conditional has to be true
b)
converse of the conditional has to be true
c)
all the above
d)
none of the above
13.

You kick your cat, and every time you do, it scratches you. You conclude that if you kick your cat you will get scratched.

a)

inductive

b)

deductive

14.
Given, "If I have a Siberian Husky, then I have a dog." Identify the inverse.
a)
If I do not have a Siberian Husky, then I do not have a dog.
b)
If I have a dog, then I have a Siberian Husky.
c)
If I do not have a dog, then I do not have a Siberian Husky.
d)
If I do not have a Siberian Husky, then I have a dog. 
15.
p→q
What is the converse?
a)
q→p
b)
∼p→∼q
c)
∼q→∼p
d)
p→∼q
16.

Is the converse True or False?

a)

False

b)

True

17.
What is the converse to this statement?
a)
If it isn't dark outside, then it is not night.
b)
If it is night, then it is dark outside
c)
If it is not night, then it is not dark outside.
d)
It is night.
18.
What phrase does a biconditional statement use?
a)
if, then
b)
if, when
c)
if and only if
d)
then, if
19.
Identify the hypothesis and conclusion of the conditional statement:
If you give me twenty dollars, then I will be your best friend.
a)
Hypothesis: I will be your best friend
Conclusion: you give me twenty dollars
b)
Hypothesis: you give me twenty dollars
Conclusion: I will be your best friend
c)
Hypothesis: if you have to pay for friends
Conclusion: then you probably should reevaluate your life
d)
Hypothesis: you will not have to pay twenty dollars
Conclusion: if you have lots of friends
20.
Complete the conjecture.  Think of examples to help.
The product of any two odd numbers is _____________
a)
even
b)
odd
c)
zero
d)
positive
21.
Describe the angle relationship.
a)
Same Side Interior
b)
Corresponding
c)
Alternate Interior
d)
Same Side Exterior
22.

Solve for the variable.

a)

x = 16

b)

x = 8

c)

x = 4

d)

x = 2

23.

Solve for the variable.

a)

x = 51

b)

x = 30.2

c)

x = 47.2

d)

x = 18.2

24.

Which proof is incorrect?

a)
b)
c)
d)
25.
What is the measure of angle b?
a)
36o
b)
56o
c)
63o
d)
117o
26.
Name the postulate, if possible, that makes the triangles congruent.
a)
SAS
b)
ASA
c)
AAS
d)
Not Possible
27.
Name the postulate, if possible, that makes the triangles congruent.
a)
SAS
b)
ASA
c)
AAS
d)
Not Possible
28.

Describe if the following triangles are congruent by choosing the appropriate postulate to support your answer.

a)

Not Congruent

b)

SAS

c)

ASA

d)

SSS

29.
State if the triangles are congruent. If they are, state how you know.
a)
SSS
b)
AAS
c)
AA
d)
Not Congruent
30.
If ∆ABC ≅∆DEF, which of the following is not a pair of congruent angles?
a)
A and D
b)
A and E
c)
E and B
d)
F and C
31.
If ∆ABC ≅∆DEF, what side is congruent to CA?
a)
FE
b)
DE
c)
FD
d)
DF
32.

In △ABC, m∠A = 3x + 1, m∠B = 4x - 17, and m∠C = 5x - 20. Which type of triangle is △ABC?

a)

Right

b)

Scalene

c)

Isosceles

d)

Equilateral

33.

Tina wants to sew a piece of fabric into a scarf in the shape of an isosceles triangle, as shown in the accompanying diagram.


What are the values of x and y?

a)

x = 42 and y = 96

b)

x = 69 and y = 69

c)

x = 90 and y = 48

d)

x = 96 and y = 42

34.
The red (ΔKNM) and blue (ΔPLM) triangles are congruent. Identify a common side or angle.
a)
Angle M
b)
Angle P
c)
Angle K
d)
Angle MLP
35.
Identify common angles or sides
a)
Angle E
b)
Angle D
c)
Angle F
d)
Angle DGF
36.
Identify any common angles or sides
a)
JK
b)
Angle MJK
c)
LK
d)
Angle MKJ
37.
Name a pair of overlapping congruent triangles and state how.  (Hint: they have to be overlapping)
a)
∆AQT ≅ ∆SQT by SAS
b)
∆TAR ≅ ∆TSP by AAS
c)
∆TAR ≅ ∆TSP by ASA
d)
∆AQT ≅ ∆SQT by SSA
38.

Given: △ABD, BC is the perpendicular bisector of AD

Which statement cannot always be proven?

a)

AC ≅ DC

b)

BC ≅ CD

c)

∠ACB ≅ ∠DCB

d)

△ABC ≅ △DBC

39.

As shown in the diagram below, CD is a median of △ABC.

Which statement is always true?

a)

AD ≅ DB

b)

AC ≅ AD

c)

∠ACD ≅ ∠CDB

d)

∠BCD ≅ ∠ACD

40.
Take a guess! Which one is the correct construction for a perpendicular bisector?
a)
1
b)
2
c)
3
d)
4
41.
A quadrilateral with 4 equal sides could be:
a)
a rectangle or a trapezoid
b)
a square or a rhombus
c)
a parallelogram or a trapezoid
d)
a kite or a square
42.
What is NOT a property of a rectangle?
a)
Diagonals are congruent.
b)
Diagonals bisect each other.
c)
Diagonals are perpendicular.
d)
All angles are congruent.
43.

If ABCD is a parallelogram, which statement would prove a that ABCD is a rectangle?

a)

∠ABC ≅ ∠CDA

b)

AC ≅ BD

c)

AC ⟂ BD

d)

∠ABD ≅ ∠DBC

44.
4 equal sides 2 pair of parallel sides diagonals bisect but are not equal in length
a)
Square
b)
Rhombus
c)
Trapezium
d)
Parallelogram
45.

What is an angle bisector?

a)

Makes two 90 degree angles

b)

Splits a 90 degree angle in half

c)

Splits any angle into 2 congruent parts

d)

Splits a side into 2 congruent parts

46.
When you draw the perpendicular bisectors of a triangle it creates the point of concurrency called the _____________.
a)
Centroid
b)
Incenter
c)
Circumcenter
d)
Orthocenter
47.
If G is the circumcenter, what type of segments are drawn?
a)
perpendicular bisectors
b)
angle bisectors
c)
altitudes
d)
centroids
48.
The figure is an example of a(n) ...
a)
angle bisector
b)
perpendicular bisector
c)
median
d)
midsegment
49.
The figure is an example of a(n) ...
a)
altitude 
b)
perpendicular bisector
c)
midsegment
d)
angle bisector
50.

What special segments are drawn in the large triangle?

a)

Median

b)

Altitude

c)

Perpendicular Bisector

d)

Angle Bisector

51.

What special segment is drawn in the large triangle?

a)

Median

b)

Altitude

c)

Perpendicular Bisector

d)

Angle Bisector

52.
Name the point of concurrency shown.
a)
Circumcenter
b)
Incenter
c)
Supercenter
d)
Neither
53.
Name the point of concurrency shown.
a)
Circumcenter
b)
Incenter
c)
Neither
d)
Center-center
54.
Name the point of concurrency
a)
incenter
b)
circumcenter
c)
centroid
d)
orthocenter
55.
Name the point of concurrency
a)
centroid
b)
orthocenter
c)
incenter
d)
circumcenter
56.
What is point J called?
a)
centroid
b)
incenter
c)
circumcenter
d)
orthocenter
57.
Where can the centroid be located on a right triangle?
a)
Outside
b)
Always inside
c)
On the hypotenuse
58.

The circumcenter of a triangle is equidistant from the _______ of the triangle.

a)

vertices

b)

sides

c)

center

d)

midsegment

59.
The circumcenter is always inside the triangle.
a)
true
b)
false
60.
Where is the circumcenter on a  obtuse triangle?
a)
Outside
b)
Inside
c)
mid point of hypotenuse
d)
at the vertex with the right angle
61.
The incenter is __________ found inside a triangle.
a)
Sometimes
b)
Always
c)
Never
62.

The incenter of a triangle is equidistant from the _________ of the triangle.

a)

midsegment

b)

center

c)

vertices

d)

sides

63.
D is the circumcenter, find ED
a)
15
b)
16
c)
17
d)
19
64.
If G is the centroid of triangle ABC and AG= 16. Find the length of GD.
a)
8
b)
16
c)
24
d)
Not Enough Information
65.
The figure is a parallelogram.  
Solve for x.  
a)
7
b)
1
c)
5
d)
2
66.
Find the measure of angle E.
a)
9°
b)
97°
c)
48°
d)
79°
67.

Which conclusion can be drawn?

a)

All quadrilaterals are kites, but all kites are not quadrilaterals.

b)

All parallelograms are rhombi, but all rhombi are not parallelograms.

c)

All squares are parallelograms, but all parallelograms are not squares.

d)

All parallelograms are rectangles, but all rectangles are not parallelograms.

68.

WXYZ is a trapezoid. Find the value of x.

a)

3

b)

5

c)

7

d)

9

69.

PQRS is an isosceles trapezoid. Find the value of x.

a)

4

b)

5

c)

6

d)

7

70.

What is the value of x in the illustration?

a)

3

b)

4

c)

5

d)

6

71.

In kite ABCD, m<DAE = 42, what is m<ABE?

a)

180°180\degree

b)

90°90\degree

c)

48°48\degree

d)

42°42\degree

72.

 In kite ABCD, m<BAD=78 and m<DBC=59. What is m<ABC?

a)

102°102\degree  

b)

59°59\degree  

c)

51°51\degree  

d)

110°110\degree  

73.

In kite ABCD, if BE = 5y-5 and ED = y+19, what is DB?

a)

6

b)

24

c)

25

d)

50

74.
If the sum of the interior angles of a polygon equals 900°, how many sides does the polygon have? 
a)
7
b)
9
c)
10
d)
12
75.
What is the value of x?
a)
26.25
b)
38.75
c)
24
d)
25.125
76.
An exterior angle of a regular polygon
measures 36°. How many sides does
the polygon have? 
a)
10
b)
5
c)
14
d)
9
77.
Find the value of x
a)
141
b)
150
c)
135
d)
163
78.
Find the sum of the interior angles in a 15-gon
a)
2000
b)
2340
c)
1875
d)
1080
79.

Analyze the graph. Using distance formula, can you prove this is a rectangle?

a)

Yes, because AD = BC = 10 and AB = CD = 5

b)

No because  AD=210AD=2\sqrt{10}  and  BC=10BC=10   

c)

Yes because AD = BC = 5 and AB = CD = 10

d)

No because  CD=73CD=\sqrt{73}  and  BC=5BC=5  

80.
What does CPCTC stand for?
a)
Congruent parts of congruent triangles are congruent
b)
Corresponding parts of congruent triangles are congruent
c)
Corresponding parts of corresponding triangles are corresponding
d)
Corresponding parts of congruent triangles are Canadian.
81.
Fill in the blank.
a)
Given
b)
Reflexive Property
c)
Transitive Property
d)
They're the same side!!!!!! 
82.
What is the "statement" for step 3 of the proof?
a)
AD=DA
b)
AN = AH
c)
HD=ND
d)
HD=DN
83.
What is the "reason" for step 2 of the proof?
a)
reflexive property
b)
proof
c)
SAS
≅ thrm
d)
given
84.
Identify the  missing statement or reason
a)
Given
b)
Vertical Angles Theorem
c)
Definition of Angle Bisector
d)
Alternate Interior Angles Theorem
85.
What is the correct choice for Statement 5?
a)
SAS
b)
Definition of Congruence
c)
Prove
d)
CPCTC
86.
What would be the correct "given" statements for this diagram?
a)
∡A≅∡C, and segment DB is the angle bisector of ∡CDA
b)
BD=BD, and DB=DB
c)
∡A≅∡C, and segment DB is the angle bisector of ∡CBA
d)
∡B≅∡D, segment DB is the angle bisector of ∡DCA.
87.
What is the "statement" for step 3 of the proof? 
a)
∡EDA≅∡DCB
b)
∡AED≅∡BEC
c)
DE=CE
d)
∡AED≅∡CED
88.

Write a plan for the proof.

Given Coordinates of vertices of △OPM and △ONM

Prove △OPM and △ONM are isosceles triangles

a)

Find the lengths of OP, PM, MN, NO and OM to show that △OMP≅△OMN by the SSS Congruence Theorem.

b)

Find the lengths of OP, PM, MN, and NO to show that OP ≅ PM and MN ≅ NO.

89.

Prove the shape is a trapezoid.

a)

The slope of the parallel bases is 4/3

b)

The slope of the parallel bases is -4/3

c)

It is not a trapezoid because the slopes do not match.

d)

It is not a trapezoid because the legs are not parallel.

90.

How would you prove a quadrilateral is a square using distance formula? (Check both)

a)

Prove there are 4 right angles

b)

Prove all 4 sides are congruent

c)

Prove diagonals are congrunt

d)

Prove opposite sides are parallel

91.

What is the distance between AB

a)

0

b)

8

c)

9

d)

7

92.

What is the distance between AB?

a)

0

b)

undefined

c)

5

d)

4

93.

How is AB written in the distance formula?

a)


d = (5−3)2 + (0−−2)2d\ =\ \sqrt{\left(5-3\right)^2\ +\ \left(0--2\right)^2}

b)

d = (2−5)2 + (3 −0)2d\ =\ \sqrt{\left(2-5\right)^2\ +\ \left(3\ -0\right)^2}

c)

d = (5−3)2 − (0−−2)2d\ =\ \sqrt{\left(5-3\right)^2\ -\ \left(0--2\right)^2}

d)

d = (4−3)2 − (2−4)2d\ =\ \sqrt{\left(4-3\right)^2\ -\ \left(2-4\right)^2}

94.

Find the midpoint of the line segment with endpoints (-2,0) & (9,-1).

a)

(1, 3)

b)

(3.5, -.5)

c)

(-.5, 3.5)

d)

(6, -.5)

95.
Write in slope intercept form
5x - 3y = -9
a)
y = (5/3)x - 3
b)
y = (5/3)x + 9
c)
y = (5/3)x + 3
d)
y = (3/5)x + 3
96.

Find the point slope form given a line with a slope of 4 going through the point (3,8)

a)

8-y=4(3-x)

b)

y-8=4(x-3)

c)

y+8=4(x+3)

d)

y-3=4(x-8)

97.
Find the equation of the line that passes through the points:

(2, 2) and (3, 4)
a)
y = 2x + 2
b)
y = -2x - 2
c)
y = -2x + 2
d)
y = 2x - 2
98.

Solve the equation by factoring.

a)

x = {3,8}

b)

x = {-3,8}

c)

x = {3,-8}

d)

x = {-3,-8}

99.

Solve the equation using the quadratic formula.


4x2 +9x = 12x

a)

x = {0, 3/4}

b)

x = {0, -3/4}

c)

x = {0, 4/3}

d)

no solution

100.
Are these two lines parallel, perpendicular or neither?
y = -1/3x - 5
y = 1/3x + 2
a)
Parallel
b)
Perpendicular
c)
Neither

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