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Geometry Final Review

Total questions: 97

Worksheet time: 1hrs 19mins

Name
Class
Date
1.

Which triangle congruence proves that the triangles are congruent?

a)

SSS

b)

SAS

c)

ASA

d)

Not Congruent

2.

Which triangle congruence proves that the triangles are congruent?

a)

SSS

b)

SAS

c)

ASA

d)

Not Congruent

3.

Which triangle congruence proves that the triangles are congruent?

a)

SSS

b)

SAS

c)

ASA

d)

Not Congruent

4.

Which triangle congruence proves that the triangles are congruent?

a)

SSS

b)

SAS

c)

ASA

d)

Not Congruent

5.

Which triangle congruence proves that the triangles are congruent?

a)

SSS

b)

SAS

c)

ASA

d)

Not Congruent

6.

Which triangle congruence proves that the triangles are congruent?

a)

SSS

b)

SAS

c)

ASA

d)

Not Congruent

7.

Which triangle congruence proves that the triangles are congruent?

a)

SSS

b)

SAS

c)

ASA

d)

Not Congruent

8.

Which triangle congruence proves that the triangles are congruent?

a)

SSS

b)

SAS

c)

ASA

d)

Not Congruent

9.

Which triangle congruence proves that the triangles are congruent?

a)

SSS

b)

SAS

c)

ASA

d)

Not Congruent

10.

Which triangle congruence proves that the triangles are congruent?

a)

SSS

b)

SAS

c)

ASA

d)

Not Congruent

11.

Which triangle congruence proves that the triangles are congruent?

a)

SSS

b)

SAS

c)

ASA

d)

Not Congruent

12.

Which triangle congruence proves that the triangles are congruent?

a)

SSS

b)

SAS

c)

ASA

d)

Not Congruent

13.

Which triangle congruence proves that the triangles are congruent?

a)

SSS

b)

SAS

c)

ASA

d)

Not Congruent

14.

What is the value of x?

(a)  

15.

What is the value of y?

(a)  

16.

What is the value of x?

HINT TO GET STARTED: What is the sum of all three angles of a triangle?

(a)  

17.

Point of Concurrency

a)

In a triangle, a line, segment, or ray that passes through the midpoint of a side and is perpendicular to that side

b)

Three or more lines that intersect at a common point.

c)

The point of intersection of concurrent lines

d)

The point of concurrency of the perpendicular bisectors of a triangle.

e)

The point of concurrency of the angle bisectors of a triangle.

18.
3 or more lines that intersect at the same point
a)
Concurrent Lines
b)
Congruent Lines
c)
Perpendicular Lines
d)
Parallel Lines
19.
Circumcenter and Incenter are these of a triangle
a)
centers
b)
vertices
c)
perpendicular bisectors
d)
angle bisectors
20.
Define: CIRCUMCENTER OF A TRAINGLE
a)
the intersection point of the three perpendicular bisectors of a triangle 
b)
when a circle passes through the three vertices of a triangle 
c)
the point of intersection of three or more lines 
d)
the intersection point of the three angle bisectors of a triangle 
21.
Define: INCENTER OF A TRIANGLE
a)
the intersection point of the three angle bisectors of a triangle 
b)
when three or more lines intersect at a single point 
c)
the intersection point of the three perpendicular bisectors of a triangle 
d)
the point of intersection of three or more lines 
22.
Which of the images represents the Circumcenter of a Triangle
a)
First
b)
Second
c)
Third
23.
Which of the images represents the Incenter of a Triangle
a)
First
b)
Second
c)
Third
24.
Name the point of concurrency shown.
a)
Circumcenter
b)
Incenter
c)
Supercenter
d)
Neither
25.
Name the point of concurrency shown.
a)
Circumcenter
b)
Incenter
c)
Supercenter
d)
Neither
26.
The figure is an example of a(n) ...
a)
angle bisector
b)
perpendicular bisector
c)
median
d)
midsegment
27.
The figure is an example of a(n) ...
a)
altitude 
b)
perpendicular bisector
c)
midsegment
d)
angle bisector
28.
Find the length of PO.
a)
32
b)
35
c)
26
d)
29
29.
Given:  AG = 10, find the length of BG.
a)
10
b)
20
c)
5
d)
30
30.
Find the length of TU
a)
15
b)
12
c)
26
d)
13
31.
1.  If m<LJK = 28°, what is m<MLK?
a)
56
b)
112
c)
62
d)
124
32.
1.  PQ  is the perpendicular bisector of MN. What is QN?
a)
7
b)
14
c)
10.5
d)
28
33.
Point P is the circumcenter, which segment is equal to PB
a)
DA
b)
AC
c)
PC
d)
PF
34.
Use the Perp Bisector Theorem to find HG
a)
28
b)
14
c)
41
d)
7
35.
Use the Perp Bisector Theorem to find PQ
a)
10
b)
3
c)
-2
d)
5
36.
Use the Perp Bisector Theorem to find  AD and  BC
a)
5;12
b)
16;4
c)
12; 16
d)
5;16
37.
Find m< JKM
a)
90
b)
76
c)
38
d)
83
38.
Find LK
a)
3
b)
5
c)
-3
d)
6
39.

Point P is the incenter of triangle PCA.

If PX is 5, what is PZ?

a)

20

b)

10

c)

5

d)

15

40.
[Angle Bisectors and Incenter]
If m<BCA is 72, what is m<PCA?
a)
72
b)
48
c)
60
d)
36
41.
[Angle Bisectors and Incenter]
If AY is 8, what is AZ?
a)
4
b)
6
c)
8
d)
10
42.

Find the value of x.

a)

2

b)

3

c)

4

d)

5

43.

Point G is the incenter of triangle ACE. What is GB?

a)

16

b)

18

c)

34

d)

50

44.
A ___________ is a quadrilateral with two sets or parallel sides and 4 congruent (equal) sides. 
a)
trapezoid
b)
rhombus
c)
parallelogram
d)
rectangle
45.
What do all of the angles of a quadrilateral have to add up to?
a)
90 degrees
b)
180 degrees
c)
270 degrees
d)
360 degrees
46.
A rectangle is also a square.
True or False?
a)
True
b)
False
47.
Which of the following properties is true about parallelograms?
a)
Base angles are congruent.
b)
Diagonals are congruent.
c)
Opposite sides are parallel.
48.
What shape is this? 
a)
Square 
b)
Rectangle 
c)
Rhombus 
d)
Parallelogram 
49.
The diagonals of a parallelogram
a)
are always congruent
b)
bisect each other
c)
are never congruent
d)
parallel
50.
A rhombus is a parallelogram with 
a)
four congruent sides
b)
four congruent diagonals
c)
four acute angles
d)
four congruent angles
51.
A rectangle is a paralellogram.
a)
True
b)
False
52.
All squares are rectangles.
a)
True
b)
False
53.
All rectangles are squares.
a)
True
b)
False
54.
A trapezoid is a paralellogram.
a)
True
b)
False
55.
All squares are rhombuses.
a)
True
b)
False
56.
The diagonals of a ________ are congruent
a)
Parallelogram
b)
Rectangle and square
c)
Rhombus and square
d)
Trapezoid
57.
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
58.
ABCD is a rhombus
What is the measurement of angle AED? 
a)
60 
b)
45
c)
90
d)
180
59.

What are the properties of a parallelogram?

a)

Opposite sides are parallel

b)

Diagonals are congruent

c)

Diagonals bisect each other

d)

All sides are congruent

e)

Consecutive angles are supplementary

60.

What are the properties of a rectangle?

a)

Four right angles

b)

Opposite sides are parallel

c)

Opposite sides are congruent

d)

Diagonals bisect each other

e)

Diagonals are congruent

61.

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

a)

Parallelogram

b)

Rectangle

c)

Square

d)

Rhombus

e)

Trapezoid

62.

Which quadrilateral(s) have four congruent sides?

a)

Parallelogram

b)

Rectangle

c)

Square

d)

Rhombus

e)

Trapezoid

63.

Which quadrilateral(s) have perpendicular diagonals?

a)

Parallelogram

b)

Rectangle

c)

Square

d)

Rhombus

e)

Trapezoid

64.

Which trigonometric ratio should you use?

a)

Tangent Ratio

b)

Sine Ratio

c)

Cosine Ratio

d)

Any ratio

65.
 Find side AB?
a)
20 m
b)
5 m
c)
11.54 m
d)
8.66 m
66.
Choose the correct ratio.
a)
A
b)
B
c)
C
d)
D
67.
Find the length of side w.
a)
21.4 cm
b)
18.0 cm
c)
36.5 cm
d)
43.6 cm
68.
Find the measure of the indicated angle (?) round to the nearest tenth.
a)
9.4
b)
55.2
c)
20.15
d)
19.4
69.
Solve for the misssing distance
a)
18.9
b)
19.5
c)
47
d)
27.5
70.
Which scenario describes the picture shown?
a)
A 5 foot ramp is 8 feet away from a building.  What is the angle that the ramp makes with the ground?
b)
A 5 foot ramp leans against an 8 foot structure.  What is the angle that the ramp makes with the ground?
c)
An 8 foot ramp leans
against a building 5 feet away.  What angle does the ramp make with the ground?
d)
A 5 foot man is 8 feet away from a building.  What is the angle of elevation?
71.
Solve for the missing angle.
a)
50.5 degrees
b)
12.7 degrees
c)
36.9 degrees
d)
72.2 degrees
72.
Solve for the triangle:
a)
AB = 14 , < A = 48.59, <B = 41.41
b)
AB = 10 , <A = 36.87 , <B= 53. 13
c)
AB = 10, <A = 53.13 , <B=36.87
73.
Find the exact value of x. 
a)
√29
b)
√7
c)
7
d)
10
74.

When the sun is 62 degrees above the horizon, a building cast a shadow 18 meters long. How tall is the building?

a)

34 m

b)

16 m

c)

9 m

d)

11 m

75.
Dustin is stuck at the top of a Ferris wheel. His mother is standing 38 feet from the base of the wheel watching him. If the angle of elevation from Dustin's mom to Dustin is 73o, how far off the ground is Dustin? 
a)
118.2 ft
b)
120.9 ft
c)
124.3 ft
d)
126.5 ft
76.
A sailing boat, which was supposed to be travelling north, veered off course and travelled N 45° E for a distance of 0.64 km, as shown. How far east had the sailing boat travelled? Give your answer to 2 decimal places.
a)
0.45 km
b)
1.28 km
c)
0.64 km
d)
1.09 km
77.
A kite is on a 300-ft string. The angle of elevation from the ground to the kite is 39°. Which is the best estimate of the height of the kite above the ground? 
a)
629 feet
b)
243 feet
c)
189 feet
d)
233 feet
78.
What is the length of x in this 45-45-90 triangle?
a)
4√2
b)
4
c)
8
d)
4√3
79.
What is the length of u and v in this 30-60-90 triangle?
a)
u = 8 v = 4√3
b)
u = 4√2 v = 8
c)
u = 16 v = 8
d)
u = 4√3 v = 8
80.
You are making a guitar pick that resembles an equilateral triangle with side lengths of 32 millimeters. What is the approximate height of the pick? (hint: use 30-60-90 theorems)
a)
32√3
b)
16√3
c)
32
d)
16√2
81.
What trigonometric ratio would be used to find the distance from the ship to the plane?
a)
sine
b)
cosine
c)
tangent
d)
inverse sine
82.
Choose the correct ratio.
a)
sin(37)=x/14
b)
cos(37)=x/14
c)
tan(37)=x/14
d)
sin(37)=14/x
83.
The angle of 12o is a(n)
a)
angle of elevation
b)
angle of depression
c)
neither
d)
both
84.
Solve for the missing angle
a)
50
b)
0.053
c)
36.9
d)
95
85.
A tourist views a deer from a height of 45 feet.  The horizontal distance between the tourist and the deer is 130 feet.  At what angle (x) should the tourist hold his camera to photograph the deer? Round your answer to the nearest degree.  
a)
19 degrees
b)
45 degrees
c)
71 degrees
d)
138 degrees 
86.

You need a ladder that will reach up a 25 foot tall house when placed 10 feet away from the house. At what angle does the ladder have to be in order to reach the top of the house?

a)

68.2 degrees

b)

21.8 degrees

c)

23.6 degrees

d)

58.9 degrees

87.
From a point 340 meters from the base of the Hoover Dam, the angle of elevation to the top of the dam is 33°. Find the height of the dam to the nearest meter. 
a)
185.18 meters
b)
523.55 meters
c)
220.80 meters
d)
624.27 meters
88.

A building 62 feet tall casts a shadow 21 feet long. At what angle is the sun shining on the building?

a)

19.80

b)

18.71

c)

70.20

d)

71.29

89.

A golfer is standing at the tee, looking up to the green on a hill. If the tee is 36 yards lower than the green and the angle of elevation from the tee to the hole is 12°, find the distance from the tee to the hole.

a)

173.15 yards

b)

7.48 yards

c)

7.65 yards

d)

169.37 yards

90.
When the angle of elevation of the sun is 78 degrees, an statue casts a shadow that is 6m long. How far is the top of the statue to the end of its shadow?
a)
1.2 m
b)
28.9 m
c)
6.1 m
d)
28.2 m
91.
From a hot air balloon 2,500ft above the ground, you see a clearing whose angle of DEPRESSION is 25 degrees.  to the nearest foot, what is your horizontal distance from the clearing?
a)
1166 feet
b)
5361 feet
c)
5916 feet
d)
2758 feet
92.
Spencer is going snowboarding.  He rode the ski lift to the top of the mountain, which is at an altitude of 1500 feet.  The angle of elevation from the bottom to the top of the mountain is 25o.  What is the length of the Spencer’s run (his trip down the hill)? 
a)
3216.76 feet
b)
633.93 feet
c)
699.46 feet
d)
3549.30
93.

After traveling a horizontal distance 400m from a runway, a plane is 300m above the ground. Calculate its angle of elevation.

a)

50

b)

0.053

c)

36.9

d)

95

94.
I am cleaning the windows on my house.  I place a 4.5 m ladder against the side of my house to reach a window that is 4 m above the ground.  What is the angle that the ladder makes with the ground? Hint: think about how a ladder leans to draw your picture.
a)
37°
b)
42°
c)
27°
d)
63°
95.
Dustin is stuck at the top of a Ferris wheel. His mother is standing 38 feet from the base of the wheel watching him. If the angle of elevation from Dustin's mom to Dustin is 73o, how far off the ground is Dustin? 
a)
118.2 ft
b)
120.9 ft
c)
124.3 ft
d)
126.5 ft
96.
An airplane takes off 600 feet in front of a 60 foot building. At what angle of elevation must the plane take off in order to avoid crashing into the building? Assume that the airplane flies in a   straight line and the angle of elevation remains constant until the airplane   flies over the building. 
a)
about .1 degree
b)
about 84 degrees
c)
about 6 degrees
d)
I love Math!
97.
The pilot of a traffic helicopter sights an accident at an angle of depression of 18 degrees.  The helicopter’s altitude is 1560 ft.  What is the horizontal distance from the helicopter to the accident? Round to the nearest foot.
a)
543 ft
b)
1756 ft
c)
4801 ft
d)
5404 ft

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