Download Geometry Semester 1 Final Exam Review

Name: __________________________________________ Date: _____________________ Per: ____
Geometry Semester 1 Final Exam Review
Chapter 1: Tools of Geometry
1)
Find a pattern for the sequence. Use the pattern to show the next three terms. 15, 12, 9, 6, …
2) If two lines intersect, then they intersect in a ___________________.
3) If two planes intersect, then they intersect in a __________________.
4) Which of the following could not be the intersection of two planes?
a.
5)
c. B
b. BA
AB
d. ABC
e. point A
B is the midpoint of AC . If AB  2 x  1 and BC  3x  4 , what is x? What is the measure of BC ? What is
the measure of AC ?
6)
Find the midpoint and distance on a number line between 6 and -15.
7) S is between R and T. If RT  64, RS  3x  1 and ST  2 x  2 , find x.
8) Draw an example of each of the following
a. Complementary
b. Supplementary
Angles
angles
9)
c. Vertical angles
mRST  2 x  8, mTSW  3x  14, mRSW  7 x  2 . Find mTSW .
10) Find mRQS .
S
2x  4
T
Q
6 x  20
R
d. Adjacent
angles
11) Find the measure of x.
3x  31
2x  6
12) Find TO given
TO  2 x  12
O
T
P
OP  x  5
TP  50
13) What is the measure of this angle?
How would you classify the angle?
14) EM bisects GEO
mGEM  3x  5
mMEO  x  29
Find mGEO .
G
15) mGIT  2x  15
mFIT  x
mGIF  4 x  5
Find mGIT .
I
T
F
16) Given the points  2, 4  and  5,1 :
a. Find the distance between the points.
b. Find the midpoint between the points.
17) Given the points  6, 5 and  3, 2  :
a. Find the distance between the points to the nearest tenth.
b. Find the midpoint between the points.
18) O is the midpoint of DG . Find the coordinate of G if O is 7 and D is 3.
19) Which is the missing endpoint if the midpoint is  0, 6  and the other endpoint is  3,8 ?
a. (1.5, 1)
b. (1, 1.5)
c. (-3, -20)
d. (20,-3)
20) I. What is the circumference of a circle with: (Leave answers in  form)
a. Radius of 4 cm
b. diameter of 32 cm
II. What is the area of a circle with: (Leave answers in  form)
b. Radius of 4 cm
b. diameter of 32 cm
21) The perimeter of a rectangle is 28 feet and the base is 8 feet. What is the height?
22) The area of a rectangle is 54 cm2 and the height is 9 cm. What is the base?
Chapter 2: Reasoning and Proof
23) Given the sentence “If you are good, then Santa will bring you presents,” write:
a.
The converse:
b. The inverse:
c. The contrapositive:
d. The biconditional:
24) Draw a conclusion:
-If a student gets an A on the final exam, then the student will pass the course.
-Felicia gets an A on the music theory final exam.
25) Draw a conclusion:
-If it is a national holiday, then school is not in session.
-If school is not in session, then students are at home.
26) Which property of equality or congruence justifies each statement?
a. If 3x  14  80 , then 3x  66 .
b. If mA  15 , then 3mA  45 .
c. If 4mC  100 , then mC  25 .
27) Solve for y.
28) Solve for x.
29) ABC and DBC are complementary. What is the mDBC if mABC  4 x 10 and mDBC  x  30 ?
30) If the supplement of T is 47 , what is the measure of T ?
Chapter 3: Parallel and Perpendicular Lines
31) Determine the relationship of the following angles.
a.
b.
c.
d.
e.
f.
1 and 2
1 and 6
3 and 6
1 and 7
1 and 5
2 and 4
4 3
1 2
5 6
7 8
32) Fill in the blank.
a.
Angles that form a linear pair ___________________________.
b. Angles that are vertical are _____________________________.
c. Corresponding angles of parallel lines are _______________________________.
d. Same-side interior angles of parallel lines are ______________________________.
e. Alternate interior angles of parallel lines are _______________________________.
33) If mA  50, mB  130, mC  50 , and they fall on parallel lines cut by a transversal
a. Which angles could be vertical?
b. Which angles could be same-side interior?
c. Which angles could be alternate interior?
34) In
FUN , the angles measure  3x  ,  2 x  20 , and  5x  5  , what is the measure of the smallest angle?
35) What is mDBA ?
B
A
C
D
36) What is the value of x?
x
37) What is the value of x?
38) If mA  60 and mB  60 ,
ABC is what kind of triangle? Classify by angles and sides.
39) If mA  45 and mB  45 ,
ABC is what kind of triangle? Classify by angles and sides.
40) Classify the triangle according to the angle and side length.
36
63
x
41) Find the missing angle measure.
a.
b.
42) Find the sum of the measures of each polygon.
a.
Dodecagon
b. nonagon
43) Find the measure of an interior angle and an exterior angle of each regular polygon.
a.
Pentagon
b. 18-gon
44) Find the slope of the line passing through the following points:
a. (-2, 3) and (-6, -5)
b. (6,9) and (-3, -8)
45) Find the slope of the line parallel to the line passing through the following points:
a. (-2, 3) and (-6, -5)
b. (6,9) and (-3, -8)
46) Find the slope of the line perpendicular to the line passing through the following points:
a. (-2, 3) and (-6, -5)
b. (6,9) and (-3, -8)
47) Determine which line is perpendicular to y 
a.
y
2
x7
3
b. y 
2
x6.
3
3
x 5
2
c. y 
3
x 8
2
d. y 
2
x6
3
48) Determine which line is parallel to y  4 x  3 .
a.
y
1
x7
4
b. y 
1
x 5
4
49) How can you determine if two lines are parallel?
50) How can you determine if two lines are perpendicular?
c. y  4 x  8
d. y  4 x  6
51) How can you determine if two lines intersect, but are not perpendicular?
52) Given AD BC , find mBDA
C
D
B
A
53) Given: l m , find x.
Chapter 4: Congruent Triangles
54) Given that IMP  OGR , name all of the pairs of  corresponding parts.
55) For each figure below, state the parts you would need to know are congruent in order to prove the triangles
congruent by the method stated.
O
A
M
a. SAS
b. AAS
I
B
C
c. HL
S
A
D
T
T
d. ASA
D
M
P
II) UY  RD
Y
T
U
56) Use the given information to make a conclusion about each figure.
U
a.
I) Y is the midpoint of RD
R
G
T
C
R
D
D
M
D
Q
A
b.
III) UY bisects RUD
U
I)
DA QU
II) What parts are congruent just by the picture?
57) Given:
JOA  ADJ
R
ON  ND
Prove: JON  ADN
O
D
N
J
A
I
58) Given: T is the midpoint of GF
GTI  FTI
Prove: G  F
G
S
59) Given: SL  CL
U
SA  AU
SC  SU
SLA is isosceles with base LA
Prove:
SCL  SUA
F
T
A
C
L
60) A is the midpoint of LU
C
S
CAL  2 x  14
SAU  3x  24
CA  x  10
L
U
A
Find the measure of SA .
61) Find x
x
62)
P
TAP is isosceles with vertex angle t.
Find mA .
T
A
63)
DAN is isosceles with base AD .
D
A
A  4 x  12
D  x  33
Find mD
N
64)
ABC is isosceles with A as the vertex angle. If mB  3x  4, mC  5x  8 . Find mB
Chapter 5: Relationships within Triangles
65) In MLK , MK is 20in. long. What is its midsegment?
66) Solve for x.
84
67) Solve for y.
D
68) a. If DF  24, BC  6, and DB  8 ,
what is the perimeter of
EBC ?
b. If the perimeter of BCE is 17,
what is the perimeter of
C
B
ADF ?
A
F
E
K
69) LJ bisects KLM , find x, JK, and JM.
J
A
M
70) AB is a median. CD = 18, BD = x-6. Solve for x.
C
B
L
D
71) G is the centroid
E
a. If GD = 7, what is AG?
b. If GC = 12, what is CF?
c. If EB = 48, what is GB?
F
A
D
G
B
C
72) In
FUN , UN  10cm, UF  16cm, and FN  14cm . Which angle is the smallest?
73) In
HAT , A  47, T  93 . List the sides in order from least to greatest.
74) Could the following be lengths of a triangle?
a. 5, 9, 13
b. 7, 14, 20
c. 1, 5, 7
d. 2, 2, 3
75) If one side of a triangle is 17 cm and the second side is 39 cm, what are the possible side lengths for the third
side?
Geometry
Semester II Review Packet #1
8.1 Ratio and Proportion
8.1
Ratio =
1.
Proportion =
3 9
Name the means.

4 12
2. Is
7 x
7 x
 equivalent to  ?
8 y
y 8
Solve proportions by cross multiplying.
extremes
3. Solve.
x 11

5 35
4. Solve.
x 2 5

x
8
means
a c

b d
5. The angles of a triangle are in the ratios
3:5:7. Find each angle measure.
6. If 2 CDs cost $14.50, how much will 15
CDs cost?
word problems – set up what is being compared
7. A 15 foot building has a 9 foot shadow.
How tall is a building with a 30 foot
shadow?
8.2 Similar Polygons
8.2
G
Similar polygons:
1) Corresponding angles are congruent.
2) Corresponding sides have equal ratios.
H
C
25
D
6
12
E
8
Scale factor = ratio of sides
A
B
20
F
ABCD ~ EFGH
8. What is the scale factor of ABCD to
EFGH?
9. Find EF, FG, and GH.
x
30
18
y
20
24
10. Find x and y.
8.3 Similar Triangles
8.3
Ways to prove similar triangles:
1) SSS~
2) SAS~
3) AA~
11. Are these triangles similar? Why?
9
12
6
8
12. Are these triangles similar? Why?
13. ABC DEF
AB  15
Find EF
AC  20
Find DE
BC  25
DF  16
8.4 Proportional Parts
8.4
Side-splitter
a
b
14. Find x and y.
15
c
a c

b d
d
10
y
24
x
52
15. Find x.
Midsegment:
1) ½ the 3rd side
2) Parallel to the 3rd side
4
x
a
b
c
d
a c

b d
16. Find x and y.
2
3
5
8
x
y
8.5 Parts of Similar Triangles
In similar triangles, the ratio of the sides is also
the ratio of the:
 Perimeters
 Medians
 Altitudes
 Angle bisectors
8.5
17. Find x and perimeter.
8
6
~
x
10
P=?
P = 28
18. Find x.
6
9
x
8
 3 3 
, 
 2 2 
Answers:
B) 
1) 3, 0, -3
2) Point
3) Line
4) C, D, E
130  11.4
17) A)
 3 3 
, 
 2 2 
B) 
5) X = 5, BC  11, AC  22
6) Midpoint: -4.5, Distance: 21
7) X = 13
8) A)
18) 11
19) C
20) IA) 8 cm
IIA) 16 cm2
B)
IB) 32 cm
IIB) 256 cm2
21) h = 6 ft
22) b = 6 cm
23) a) If Santa brings you presents, then you
were good
C)
b) If you are not good, then Santa will
not bring you presents
1
2
c) If Santa does not bring you presents,
then you were not good
d) Santa will bring you presents if and
only if you are good
D)
24) Felicia will pass the course
9) X = 12, mTSW  50
10) X = 19.5, mRQS  137
11) X = 31
12) X = 11, TO  34
13)
14) X = 12, mGEO  82
15) X = 10, mGIT  35
16) A)
74  8.60
25) If it is a national holiday, then students are
at home
26) a) Subtraction property of equality
b) Multiplication property of equality
c) Division property of equality
d) Symmetric property of congruence
27) y = 18
28) x = 6
29) x = 14, mDBC  44
42) a) 1800
30) mT  133
43) a) interior = 108, exterior = 72
b) interior = 160, exterior = 20
31) a) Supplementary angles
b) Alternate interior angles
b) 1260
44) a) m = 2
b) m 
17
9
45) a) m = 2
b) m 
17
9
b) m 
9
17
c) Corresponding angles
d) Corresponding angles
e) Same-side interior angles
f) Vertical angles
32) a) are supplementary
46) a) m 
1
2
47) C
b) Congruent
48) D
c) Congruent
49) If the slopes are the same
d) Supplementary
50) If the slope are opposite reciprocals
e) Congruent
51) The slopes are different by not opposite
reciprocals
33) a) A, C
b) A, B, and C, B
52) mBDA  40
53) x = 20
c) A, C
34) x = 15,5, smallest angle = 46.5
35) mDBA  110
36) x  70
37) x = 50
54) I  O, M  G, P  R
IM  OG, MP  GR, IP  OR
55) A) BI  MD
B) T  G
38) Equiangular and equilateral
C) RM  RS
39) Right and isosceles
D) MUP  DPU
40) Acute and scalene
41) a) y  102
b) n = 113, n+6=119
56) AI) RY  YD
AII) mUYD  mUYR  90
AIII) RUY  DUY
57)
BI) DAQ  UQA
63) x = 15, mD  48
BII) QA  QA reflexive property
64) x = 6, mB  22
Statement
65) 10 in
Reason
66) x = 23
JOA  ADJ
Given
ON  ND
Given
ONJ  DNA
Vertical angles
JON  ADN
67) y = 7
68) a) 52 units
b) 34 units
69) x = 12, JK = 17, JM = 17
ASA
70) x = 15
58)
Statement
Reason
71) a) 14
T is the midpoint of GF
Given
GTI  FTI
Given
TI  TI
Reflexive
74) a) yes
c) no
CPCTC
75) 22  x  56
Reason
8.1
SL  CL
Given
SA  AU
Given
SC  SU
Given
1)
2)
3)
4)
5)
6)
7)
8)
9)
4&9
3 & 12
no
16/3
12
108.75
50 ft
4:3
EF =15
FG = 9
GH = 75/4
10) x = 16, y=12
SLA is isosceles Given
CLS and UAS Definition perpendicular
are right angles
lines
CLS  UAS
All rt. Angles are
congruent
SCL  SUA
60) x = 38, SA = 28
HL
8.3
61) x – 80
62) mA  62.5
b) yes
SAS
G  F
Statement
72) F
73) AT , HT , AH
GTI  FTI
59)
b) 18
11) yes, SAS~
12) yes, AA
d) yes
c) 16
13) EF = 20, DE = 12
8.4
14) x = 16, y = 20
15) x = 8
16) x = 12, y = 20
8.5
17) x = 7.5, P = 21
18) x = 12