Download 1st Semester Practice Final Name: ______ ____ Date: Period

1st Semester Practice Final
Name: __________
____
Date:
Period: _________
1st Semester Final
Score
Grade
Multiple Choice & Fill in the Blank
/
/
1.1 Angle Relationships
Pr 1, 2, 3, 5, 9
/ 16pts /
1.2 Triangle Angle Relationships Pr, 4, 10, 11, 12, 13, 14
/ 11pts /
2.1 Pythagorean Theorem Pr 15, 16
/ 4 pts /
2.2 Right Triangle Trig
Pr 17, 18, 19, 20, 21
/ 10 pts /
2.3 Special Right Triangles Pr 22, 23, 24
/ 11 pts /
3.1 Standard Transformations Pr 6, 7, 8
/ 6 pts /
4.1 Prove Triangle Similarity Pr 29, 30
/ 8pts /
4.2 Triangle Congruency
Pr 25, 26, 27, 28
/ 17pts /
5.1 Angles in a Regular Polygon Pr 31, 32
Final Score
/ 18 pts /
/ 101 pts /
1. Given parallel lines cut by a transversal, alternate-side exterior angles are . . . (Circle any
that apply 1 point)
Congruent
Supplementary Complementary
Corresponding
Adjacent
Hypotenuse
2. Two angles are complementary if they… (Circle any that apply 1 point)
Are equal
Are congruent
Are inside parallel lines
Add to 180
Add to 90
3. For each diagram find the value of x. (3 points each)
Show your work and name the angle relationship(s) you used to solve the problem.
a)
b)
15x
–x + 20
5x + 10
4x – 40
Show Work and Name Relationship(s)
Show Work and Name Relationship(s)
1st Semester Practice Final
Name: __________
____
Date:
Period: _________
4. For the diagram find the value of x. Show your work. (2 points)
45°
120°
x°
5. Find all the values of the variables shown below.
f
s
j
x
t
r
m
150
60
(7 points)
f=
j=
x=
s=
r=
t=
m=
6. What are the new coordinates after you translate PQR 2 units down and 5 units to the left.
A) P'(3, 4) Q'(4, 1) R'(7, 1)
B) P'(-7, 0) Q'(-6, -3) R'(-3, -3)
P
C) P'(0, 7) Q'(1, 4) R'(4, 4)
Q
R
D) None of these.
1st Semester Practice Final
Name: __________
____
Date:
Period: _________
7. What are the coordinates of B' after the ∆ABC is dilated about the origin with a zoom factor of 2.
A) B'(10, 4)
A(1,2)
B(5,2)
C(3,3)
B) B'(15, 2)
C) B'(5, 6)
D) None of these
8. The point A(6, -4) is rotated 90 counter-clockwise about the origin.
The coordinate of A is:
A)
B)
C)
D)
(-4, 6)
(-4, -6)
(-6, 4)
(4, 6)
9. Given parallel lines cut by a transversal, alternate interior angles are ?
A) Perpendicular
B) Complementary
C) Congruent
D) Supplementary
10. In the figure below, find the measures of 1, 2, and 3. (3 points)
2 63º
3
1
1st Semester Practice Final
Name: __________
____
Date:
Period: _________
11. Choose a value for x such that will make this a true triangle.
(1 Point)
x
8
21
A) x = 13
B) x = 29
C) x = 14
D) x = 32
12. Solve for the measure of x in the diagram to the right. (1 Point)
19
A) 128°
B) 52°
14
C) 19°
x
D) 33°
13. Given isosceles triangle ∆ABC with AB = AC. If A = x + 17
and B = 2x + 4 then C = ? (2 Points)
A
x + 17
A) 7o
B) 16o
C
C) 30o
D) 66o
2x + 4
B
E) None of These
14. Find the value of x in the triangle to the right. (2 Points)
A) 61 in
B) 69.31 in
C) 119.101 in
D) 97.86 in
x
109
.12
40
48"
1st Semester Practice Final
Name: __________
____
Date:
Period: _________
15. Use the Pythagorean Theorem to show whether or not the given lengths of the sides are correct.
Is it a right triangle? Circle the correct answer. (2 Points)
Show your work.
22
Yes or No
25
5
16. Find the value of x in the triangle to the right. (2 Points)
A) 12.1 units
15.199
B) 9.8 units
5
C) 6 units
x
D) 16 units
6
17. Solve for θ in the following triangle. (2 Points)
A) 60°
B) 0.37°
12
C) 68.68°
°
D) 30°
Using trigonometric ratios solve for the missing measurement in the triangles below. (2 Points each)
33°
18.
A) 52.9
130
k
B) 200.182
C) 118.8
D) 84.42
19.
A) 8.99
14
B) 21.78
y
40
C) 15.66
D) 18.66
1st Semester Practice Final
Name: __________
____
5
20.
8
Date:
Period: _________
A) 32°
B) 39°
θ
C) 51°
D) 58°
21. Brett is 45 feet from the base of a building. He measures the angle of elevation to the top of the
building and finds it is 40°. How tall is the building? (2 Points)
A) 412.35 feet
B) 37.76 feet
C) 53.629 feet
D) None of these
22. Fill in the blank with the missing length(s) in each of these triangles. You must express your
answers in simple radical form. (4 points)
_______
_______
30
24
60
_______
45
_______
23. a. Draw the 45/45/90 triangle ∆𝑃𝑄𝑅 below. Label the angles and side lengths.
b. Given that the leg of ∆𝑃𝑄𝑅 is 6in, find the lengths of the remaining sides.
1st Semester Practice Final
Name: __________
____
Date:
Period: _________
24. If the sides of a triangle are 12, 6√2, & 6√2;
a. Draw and label a picture of this triangle. (1 point)
b. Is this a 30/60/90 or a 45/45/90 triangle? Justify (prove) your response. (2 point)
25. Complete the following proof. (5 points)
Statements
Reasons
1. QD  AU
D
A
1.
2.
Q
U
2. Given
3. DU  UD
3.
4. ∆QDU  ∆AUD
4.
26. For each pair of triangles, decide whether or not they are congruent. If they are congruent, write
the congruent statement (ABC ≅  . . .) and the congruence property (SSS, etc.) that
proves it. If not, say "not ≅’. NOTE: These are not to scale! (4 points)
a. PQR ≅ _________
by
.
HJK ≅ __________by
.
H
Q
V
R
b.
P
S
M
U
J
K
L
1st Semester Practice Final
Name: __________
____
Date:
Period: _________
27. . Prove the following by completing the two column proof below. (6 points)
Given:
TR  RE
TRK  ERK
Prove:
T  E
R
Statements
Justifications
K
1. TR  RE
1.
2.
2. Given
3.
3.
4. ∆TRK  ∆ERK
4.
5. T  E
5.
T
28. Complete the following proof. (5 points)
D
Given: E is the midpoint of AC
DE  EB
A
A
E
B
Prove: ∆AED  ∆CEB
E
C
Statement
Reason
1.
1. Given
2. E is the midpoint of AC
2.
3.
3. Definition of midpoint
4.
4. Vertical angles are equal
5. ∆AED  ∆CEB
5.
1st Semester Practice Final
Name: __________
____
Date:
Period: _________
29. Given ABC~WYZ, which of the following could be used to solve for x? (7 point)
B
x
Z
A
8
C
40
15
W
20
Y
Proportions/Equation
Correct
Not Correct
𝑥
40
=
20
8
20𝑥 = 40
𝑥
8
=
40 20
𝑥 40
=
8 20
8𝑥 = 128
𝑥 15
=
8 20
8
𝑥
=
20 40
30. Given the triangles to the right, what conjecture
can be used to show DEF~TRV? (1 point)
T
A) SSA~
F
14
B) SAS~
C) ASA~
D) Not ~
78
D
78
E
6
R
21
9
V
1st Semester Practice Final
Name: __________
____
Date:
Period: _________
31.Fill in the table below with the correct missing information for each regular polygon.
(15 points)
Number of Sides
Single Interior Angle
Single Exterior Angle
Sum of Interior
Angles
10
2700°
72°
20°
N
32. Use what you have learned about the angles of a polygon to write an equation and solve for
the unknown variable. Show all work. (3 points)
110
(x + 20)
x