Download Geometry Fall Final Review

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Block
Geometry Fall Final Review
Unit 1
1) Points H, G, and J are collinear, and G is in
between H and J. If HG = 3x - 4, HJ = 4x + 3, and GJ
= 3x + 4, what is HJ?
13) The measure of two supplementary angles are
(3x – 10) and (6x + 100). Find the measure of the
smaller angle.
2) P is the midpoint of AB. If AP = 3n and
AB = 5n + 2, find the length of AB.
14) What is the measure of EFG if
 EFH = 111°?
4) SU bisects RST. If RST = (8x + 15) and
RSU = 5x°, find RST.
H
G
3) KL bisects VKW. Classify VKW as acute,
obtuse, right or straight if LKW = 25.
(3x + 5)
(3x + 20)
E
F
15)  KLM and RST are complementary angles.
KLM= (7x) and  RST= ( 36 – x). Find the
measure of the smaller angle.
E
D
16) Solve for x.
17
F
25
x
A
C
B
For questions 5 - 7
5) What is the measure of  ABC?
6) What is the measure of  DBC?
7) What is the measure of  EBD?
T
Q
18) T is the midpoint of RS. T has coordinates (6, 4), and S has coordinates (3, -2). Find the coordinates
of R.
19) What is the distance between the points
(6, -7) and (1, 5)?
S
R
17) M is the midpoint of PQ, P has coordinates
(-7, 2), and Q has coordinates (0, -5). Find the
coordinates of M.
P
For questions 8 - 9
U
8) Name an angle that is a supplement
of  RPS.
Unit 2
20) Find the coordinates of A(-2, 4) after the
translation (x, y)(x - 8, y + 7).
21) Find the coordinates of the image of K(-8, 7)
after the translation (x, y)→ (x – 10, y – 2).
9) Name a pair of vertical angles.
10) If the complement of an angle measures 22°,
what is the measure of its supplement?
11) Two vertical angles are also complementary.
Find the measure of one of the two vertical angles.
12) Two angles form a linear pair. One angle
measures (10x – 63). The other angle measures
(8x)°. What is the value of x?
22) Describe the transformation as a reflection,
translation or rotation.
23) ΔABC is translated so that it becomes ΔA’B’C’.
Translate ΔDEF using the same rule.
27) Translate
(x, y)→(x + 5, y – 3)
24) a. Reflect ΔABC over the x- axis. Label it
ΔA’B’C’.
28) Write the rule for each transformation. If it is a
reflection, state the line of reflection. If it is a
translation, state the rule using arrow notation. If it is
a rotation, name the center of rotation, the angle of
rotation, and the direction of rotation.
a.
b. Reflect ΔA’B’C’ over the y-axis. Label it
ΔA’’B’’C’’,
c. What transformation could map ΔABC onto
ΔA’’B’’C’’ in one transformation? Be specific.
b.
25) Rotation 90°
counter-clockwise
around the origin.
c.
26) Reflection across
the line y = x.
29) Show that line DE is the line of reflection by:
36) If j ll k, solve for x.
a. showing that BB ' is perpendicular to DE .
(3x – 15)
b. showing that the midpoint of BB ' lies on DE .
(2x + 10)
j
k
37)
a. Find the measure of  1.
b. What idea or theorem helped you find this
measure?
38) Find the possible values for x.
x
358'
132'
Unit 3
n
l
______ < x < _______
1 4
2 3
5 8
6 7
39) Write a correct congruence statement.
C
a.
O
For questions 30-33
30) Name an angle that is alternate interior angle
with 4.
31) Name a pair of corresponding angles.
A
T
G
D
b.
O
W
32) Name a pair a pair of same-side interior angles.
G
33) Name the angle that must be congruent to 8 to
prove that l ll n. Justify your answer
F
34) If lines p and q are parallel, find the value
of x.
p
q
B
I
T
X
3x°
c.
(x + 90)°
M
35) If ∆PQR  ∆STU, name the angle that is
congruent to  SUT.
O
F
I
40) In the figure, X  Z and WX = YZ. Can you
prove WXU  YZU? Explain.
Y
44) Complete the proof.
Given: MN ll PO ,
MO
X
Congruent Sides
or Angle Pairs
U
N
O
M
P
Reasons
Z
W
Determine whether or not the following triangles are
congruent. If they are, finish the congruence
statement and tell which theorem you used to
determine your answer. If not, say “not enough
information.”
41)
NOP   ______ by ____________
X
W
45) Complete the proof.
Given:  A   D,
AC  CD
Y
Z
ΔZWY  Δ______ by______
42)
Congruent Sides
or Angle Pairs
X
W
Y
Z
ΔWXZ  Δ______ by______
43)
A
B
X
C
Reasons
ABC   ______ by ____________
46) Considering the triangles in the above proof, is
AB  DE ? Explain.
47) Given the figure, explain why BC  QR.
D
P
A
ΔABX  Δ______ by______
B
C
R
48) QS bisects  PQR. Find QR.
P
5x
5x - 10
Q
S
5x
3x + 16
R
Q
49) Complete the proof.
Given:  DCA   BCA
BD
(3x – 11) (2x + 5)
C
Congruent Side
or Angle Pairs
56)
B
Reasons
A
57)
D
58)
3x - 10
2x + 30
59)
2x + 30
3x - 10
ABC   ______ by ____________
Mixed Review
For problems 25 – 38, write an equation to solve
for x, then justify your reasoning.
50)
60)
61)
2x + 2
5x - 10
51)
62)
52)
63)
53)
54)
(5x – 16) (3x + 4)
55)
64) Sketch an example of each of the following terms:
a. exterior angle
b. line
c. ray
d. parallel lines
e. perpendicular lines
f. vertical angles
g. linear pair
h. perpendicular
bisector
i. angle bisector
j. adjacent angles
k. right triangle
l. line segment
m. vertex
n. remote interior angles
o. parallel planes
(highlight)
p. isosceles triangle
q. supplementary angles
r. straight Angle
s. obtuse angle
t. corresponding angles
u. complementary
angles
v. alternate interior
angles
w. acute angle
Construct the following. Show all construction marks.
65) An angle congruent to  ABC.
A
C
B
66) the angle bisector to  PQR
67) The perpendicular bisector of segment FM.
P
F
Q
R
68) A line parallel to line t through point P.
69) Construct the line of reflection.
P
t
70) Construct the rotation: RA, 115°
71) Construct the center of rotation.
Y
X
Z
•
A
M