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High School Geometry Final

Total questions: 65

Worksheet time: 2hrs 12mins

Name
Class
Date
1.
Are these triangles congruent?
a)
Yes, by ASA
b)
Yes, by SAS
c)
No they are not congruent
d)
Not enough information to know for sure
2.

If ∆LMK ≅ ∆LMT, then ∠K ≅ ____ 

a)

LL  

b)

∠L\angle L  

c)

∠T\angle T  

d)

T

3.

Given 

ΔABC ≅ΔDEF \Delta ABC\ \cong\Delta DEF\   BC‾ ≅ ?\overline{BC}\ \cong\ ?  

a)

DE‾\overline{DE}  

b)

EF‾\overline{EF}  

c)

DF‾\overline{DF}  

d)

FD‾\overline{FD}  

4.

Solve for the value of X.

X= (a)  

5.
What are the five ways to prove triangles congruent?
a)
SSS, ASA, AAS, SAS, HL
b)
SSS, SSA, HL, AAS, SAS
c)
SAS, SSA, HL, AAS, SSS
d)
HL, SAS, SSA, SSS, ASA
6.
Identify the transformation from ABCD to A'B'C'D'.
a)
Translation
b)
Reflection across the x-axis
c)
Reflection across the y-axis
d)
90o counter clockwise rotation
7.
Determine how to translate triangle A'B'C' to triangle ABC.
a)
right two, down five
b)
right two, down 9
c)
left two, down 9
d)
left two, down 5
8.
If a line segment has a length of 12 units and after a dilation the image length is 4 units, what was the scale factor?
a)
3
b)
1/3
c)
8
9.
Dilate the figure by a scale factor of 3 with the origin as the center of dilation. What are the coordinates of the image?
A(3,3) B(6,6) C(9,3)
a)
A'(9,9) B'(18,18) C'(27,9)
b)
A'(6,6) B'(9,9) C'(12,6)
c)
A'(0,0) B'(3,3) C'(6,0)
d)
A'(1,1) B'(2,2) C'(3,1)
10.

An isosceles triangle has _________ equal sides.

a)

one

b)

two

c)

three

d)

four

11.

Which type of triangle is pictured?

a)

A

b)

B

c)

C

d)

D

12.

Which type of triangle is pictured?

a)

A

b)

B

c)

C

d)

D

13.

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

14.

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

If it is water, then it is wet.

a)

If it is not wet, then it is not water.

b)

If it is wet, then it is water.

c)

It is water if and only if (iff) it is wet.

d)

There is no biconditional statement.

15.

What is the justification?

a)

Definition of Supplementary Angles

b)

Vertical Angles Theorem

c)

Definition of an Angle Bisector

d)

Angle Addition Postulate

16.

What is the justification?

a)

Segment Addition Postulate

b)

Definition of Midpoint

c)

Addition Property of Equality

d)

Complement Theorem

17.

What is the justification?

a)

Definition of an Angle Bisector

b)

Complementary Angles Theorem

c)

Definition of a Right Angle

d)

Angle Addition Postulate

18.
What is the missing statement in the proof?
a)

2m∠ABD=m∠ABD+m∠ABD

b)

m∠ABD=m∠DBC

c)

m∠ABC=m∠ABC

d)

m∠ABD+m∠ABD=m∠ABD+m∠DBC

19.

x + y = 10

given: y = 4

Which is true?

a)

x + 4 = 10 by substitution property of equality

b)

4 + y = 10 by substitution property of equality

c)

x = 6 by substitution property of equality

20.

In the graph below, ΔMNO is the image of Δ𝐵AC after a

rotation of 270° counterclockwise about the origin.

Which statements below are true? Select all that apply.

a)
b)
c)
d)
e)
21.

Determine whether the polygons are similar, if they are, write the similarity statement and find the scale factor from figure A to Figure B.

a)

Yes they are Similiar,

k=2.5k=2.5

b)

YEs they are Similiar, k=0.4k=0.4

c)

Not similar

22.

The larger Popsicle is a dilation of the smaller Popsicle stick. Select all statements that are true.

a)

The scale factor of the dilation is 32\frac{3}{2}

b)

Point L is the center of Dilation

c)

ΔLOV∼ΔLEY\Delta LOV\sim\Delta LEY

d)

3(LV)=2(LY)3\left(LV\right)=2\left(LY\right)

e)

LOOE=OVEY\frac{LO}{OE}=\frac{OV}{EY}

23.

7.) What is the scale factor of the dilation from A to B ?

a)

2

b)

1

c)

1/2

d)

1/3

24.

Which of the below is the only correct similarity statement for the two triangles?

a)

ΔSKE∼ΔTHC\Delta SKE\sim\Delta THC  

b)

ΔSKE∼ΔTCH\Delta SKE\sim\Delta TCH  

c)

ΔSKE∼ΔCHT\Delta SKE\sim\Delta CHT  

d)

ΔSKE∼ΔHCT\Delta SKE\sim\Delta HCT  

25.

Identify which triangles can be proven similar using the SSS Theorem. Mark all that apply.

a)
b)
c)
26.

Identify which of the following triangles are similar by SAS Theorem.

a)
b)
c)
27.

Using (SSS, AA, SAS) can you determine must be similar? If so, explain why.

a)

Yes, by SSS

b)

Yes, by AA

c)

Yes, by SAS

d)

There is not enough information to prove similarity

28.

Set up an equation that could be used to solve for the variable.

a)
b)
c)
d)
29.

Set up an equation that could be used to solve for the variable.

a)
b)
c)
d)
30.
Find the measure of the missing angle.
a)
64o
b)
26o
c)
61o
d)
8o
31.
Solve for the missing angle
a)
50.5 degrees
b)
12.7 degrees
c)
36.9 degrees
d)
72.2 degrees
32.

Find the length of side AC.

a)

25.4

b)

24.7

c)

29.2

d)

28.3

33.

Focus in on the 70o angle...which two sides are "identified" in the figure?

a)

opposite

(an unknown)

b)

hypotenuse

(4 units)

c)

adjacent

(no marking)

d)

None of these

34.

So we should have found;

opposite side = ?

hypotenuse = 4

(remember...related to the 70o angle!!!) Which trig ratio uses these two sides?

a)

sine (sin)

b)

cosine (cos)

c)

tangent (tan)

d)

None of these

35.

Let's consider angle B (25o). Which two sides do "b" and "8" represent?

a)

Opposite

b)

Adjacent

c)

Hyptonuse

d)

All of them

36.

Let's focus on these two;

Opposite Side = "b"

Adjacent Side = "8"

(in relationship to angle B)

Which trig ratio uses these two sides?

a)

sine (sin)

b)

cosine (cos)

c)

tangent (tan)

d)

none of them

37.

Which of the following best represents the length of side "b?"

a)

3.73

b)

177.88

c)

17.16

d)

17.74

38.

Choose the correct set up to find the length of the side x.

a)

sin⁡(37°)=x14\sin\left(37\degree\right)=\frac{x}{14}  

b)

cos⁡(37°)=x14\cos\left(37\degree\right)=\frac{x}{14}  

c)

tan⁡(37°)=x14\tan\left(37\degree\right)=\frac{x}{14}  

d)

None of these are correct

39.

What is the measure of the angle "?"

a)

70º

b)

90º

c)

105º

d)

210º

40.
Solve for x
a)
6
b)
7
c)
8
d)
9
41.
What is the value of x and y?
a)
x=75°; y=93°
b)
x=65°;y=104°
c)
x=75°; y=94°
d)
x=65°; y=93
42.
In circle O, the radius is 4, and the measure of minor arc AB is 120 degrees. Find the length of minor arc AB to the nearest integer.
a)
5
b)
9
c)
8
d)
6
43.
Find the arc length.  Leave your answer in terms of π.
a)
7/4π
b)
7/2π
c)
1/8π
d)
45π
44.
Find the area of the shaded sector of circle O.  The radius is 6 inches and the central angle is 100°.  Express answer to the nearest tenth of a square inch.
a)
9.2 sq. in.
b)
10.5 sq. in.
c)
31.4 sq. in.
d)
38.2 sq. in.
45.
Find the area of the dark blue sector shown at the left.  The radius of the circle is 4 units and the length of the arc (the curved edge of the sector) measures 7.85 units.  Express answer to thenearest tenth of a square unit.
a)
0.3 square units
b)
15.7 square units
c)
19.7 square units
d)
50.3 square units
46.

Which is the center of the circle with the equation

(x - 3)2 + (y + 5)2 = 16

a)

(3, 5)

b)

(-3, 5)

c)

(5, -3)

d)

(3, -5)

47.

Which is the radius of the circle with equation

(x - 2)2 + (y + 4)2 = 9

a)

81

b)

3

c)

9

d)

4.5

48.
a)

(x + 2)2 + (y - 1)2 = 2

b)

(x + 2)2 + (y - 1)2 = 1

c)

(x - 2)2 + (y + 1)2 = 1

d)

(x + 2)2 + (y - 2)2 = 1

49.

Select the figure that makes lines r and t parallel.

a)
b)
c)
d)
50.
a)

No

b)

Yes, Corresponding angles are congruent

c)

Yes, Alternate Interior angles are congruent

d)

Yes, Alternate Exterior angles are congruent

51.
a)

No

b)

Yes, Corresponding angles are congruent

c)

Yes, Alternate Interior angles are congruent

d)

Yes, Alternate Exterior angles are congruent

52.
What is the formula for the volume of a cone?
a)
V = (1/3)P*h
b)
V = (4/3)πr3
c)
V = πr2 + πrl
d)
V = (1/3)πr2h
53.
What is the formula for the volume of a prism?
a)
V = P*h
b)
V = B*h
c)
V = (1/3)P*h
d)
V = (1/3)B*h
54.
What is the formula for the surface area of a pyramid?
a)
SA = 2B + P*h
b)
SA = B + P*h
c)
SA = 2B + (1/2)P*l
d)
SA = B + (1/2)P*l
55.

If the rectangle above is continuously rotated about side w, which solid figure is formed?

a)

pyramid

b)

rectangular prism

c)

cone

d)

cylinder

56.

Triangle ABC represents a metal flag on pole AD. On a windy day the triangle spins around the pole so fast that it looks like a three-dimensional shape. Which shape would the spinning flag create?

a)

sphere

b)

pyramid

c)

right circular cylinder

d)

cone

57.

An isosceles right triangle whose legs measure 6 is continuously rotated about one of its legs to form a three-dimensional object. The three-dimensional object is a

a)

cylinder with a diameter of 6

b)

cylinder with a diameter of 12

c)

cone with a diameter of 6

d)

cone with a diameter of 12

58.

Triangle ABC, with vertices at A(0,0), B(3,5), C(0,5) and , is graphed. Which figure is formed when ΔABC is rotated continuously about BC?

a)
b)
c)
d)
59.

A rectangle whose length and width are 10 and 6, respectively, is shown. The rectangle is continuously rotated around a straight line to form an object whose volume is 150π.

a)

a long side

b)

a short side

c)

the vertical line of symmetry

d)

the horizontal line of symmetry

60.
What is the total surface area of the triangular prism shown? 
a)
468 in2
b)
540 in2
c)
576 in2
d)
700 in2
61.
What is the surface area of the cylinder to the nearest square inch? 
a)
625 in2
b)
1300 in2
c)
1046 in2
d)
414 in2
62.
Find the area of each sector.
a)
52.4 in2
b)
18,864 in2
c)
60 in2
d)
10.47 in
63.
A cathedral window is built in the shape of a semicircle. If the window is to contain three stained glass sections of equal size, what is the area of each stained glass section?  Express answer to the nearest square foot.
a)
1 sq. ft
b)
13 sq. ft
c)
3 sq. ft
d)
26 sq. ft
64.
Find the volume of the given figure. encuentra el volumen
a)
308.9 cm3
b)
308.2 cm3
c)
312.8 cm3
d)
302.9 cm3
65.
Find the volume of the solid.
a)
1043 in³
b)
1323 in³
c)
1008 in³
d)
903 in³

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