Download Midterm Review Part 3

Proofs
R
1.
Given: RF  AT
F is a midpoint of AT
Prove:
AFR  TFR
A
T
F
Statements
1. ___________________________
2. ___________________________
3. ___________________________
4. ___________________________
5. ___________________________
6. ___________________________
7. ____________________________
Reasons
1._______________________________________________________
2._______________________________________________________
3._______________________________________________________
4._______________________________________________________
5._______________________________________________________
6. ______________________________________________________
7.________________________________________________________
E
D
B
2.
Given: EA DC
Prove:
EBA  CBD
EB  BC
Statements
1. ____________________________
2. ____________________________
3. ____________________________
4. ____________________________
C
A
Reasons
1. _____________________________________________________
2. _____________________________________________________
3. _____________________________________________________
4. ______________________________________________________
Y
Z
3.
Given: W is a midpoint of ZX
Prove: ZV YX
W
VW  WY
V
Statements
1. ___________________________
2. ___________________________
3. ___________________________
4. ___________________________
5. ___________________________
6. ___________________________
7. ____________________________
X
Reasons
1. ______________________________________________________
2. ______________________________________________________
3. ______________________________________________________
4. ______________________________________________________
5. ______________________________________________________
6. ______________________________________________________
7._______________________________________________________
Geometry Mid-Term Review 2006 – 2007
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4.
Given: 3(2x – 5) + 1 = 2(x – 3)
Prove: x = 2
Statements
1.___________________________
2.___________________________
3.___________________________
4.___________________________
5.___________________________
6.___________________________
Reasons
1.__________________________________
2.__________________________________
3.__________________________________
4.__________________________________
5.__________________________________
6.__________________________________
c
5.
Given: a  b
1  4
d
1
a
2
Prove: c  d
3
b
4
Statements
1.
2.
3.
4.
5.
6.
a  b
1  3
3  1
1  4
3  4
c  d
Reasons
1.__________________________________
2.__________________________________
3.__________________________________
4.__________________________________
5.__________________________________
6.__________________________________
Geometry Mid-Term Review 2006 – 2007
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Part I. Fill in the blank.
1. A line segment contains ______________________________________________________.
2. If AM = MB and points A, M and B are collinear, then ______________________________________________.
3. In a triangle, the smallest angle is (where?) _______________________________________________________ .
4. If two parallel lines are cut by a transversal, all corresponding angles are ___________.
5. If A is between B and C and are collinear, then _______________________________ .
6. A right triangle has (what types of angels?)___________________________ and ________________________ .
7. ________________________________________________ (7) are methods to prove triangles congruent.
8. The intersection of two planes is a ____________________.
9. In quadrant ___________, the x and y coordinates are both negative.
10. Acute angles measure _____________________________________.
11. Equiangular triangles are also ____________________________.
12. Parallel lines have the same _________________.
13. The intersection of two lines is a ___________________________.
14. If two angles are supplements of congruent angles, then the two angles ___________.
15. Corresponding sides of congruent triangles __________________________.
16. Skew lines are __________________________ and ___________________________ .
17. The slope of a horizontal line is _____________ .
18. Two angles are complementary if ________________________________________________________ .
19. The angles in a triangle sum to _________________ .
20. Vertical angles are ____________ and____________________________________________________________ .
21. An isosceles triangle has _________________ and ________________________________________________ .
22. An equilateral triangle has ____________________ and ______________________________________________
23. If a conditional statement is false, then so is its _____________________________________ .
24. The hypotenuse of a right triangle is opposite the ________________________________________________.
25. If two sides of a triangle have length 4and 6 then the third side must be __________________________.
26. A(n) _____________________ of a right triangle is the longest side.
27. The slope of a vertical line is _____________________ .
28. In a triangle, the largest angle is ______________________________________________________.
29. Two lines that are not parallel or skew are _____________________ or _____________________________.
30. The three medians of a triangle intersect ____________________________ and _______________________.
31. When two parallel lines are cut by a transversal, the exterior angles are ______________or _______________.
Geometry Mid-Term Review 2006 – 2007
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32. If two lines are parallel, then alternate interior angles are __________________.
A
Part II. Free response by chapter.
True or false.
B
l
C
D
Chapter 1
1. Points A, B and H are collinear. _____
2. Point A lies on line m. _____
3. Points B, C and H are coplanar. _____
I
G
H
4. Points E, J and F are collinear. _____
E
5. Point C lines on line l. ______
m
J
F
6. Plane ABC and plane BCF intersect at point B. _____
For questions 7 – 11, refer to the diagram at the right.
7. Name the intersection of CD and plane P. _____________
8. If TB and TC were drawn, what would be their intersection? ______
9. Name the intersection of line l and CD . ______________
10. Name four noncoplanar points. _____________________
11. Write another name for plane P. ____________________
T l
A B
P
C
D
For questions 12, write the following using symbols. Do not draw.
12.
a. perpendicular ________
d. parallel ________
g. ray KL ________
a. line segment AB ________ e. the length of line segment CD ________
b. angle EFG ________
f. the measure of angle HIJ _____________
13. Find the length of the segment with endpoints H(2, 3) and J(6, 7). ____________________
14. Find the midpoint of the segment MN with endpoints M(8, 9) and N(-2, 1). ________________
For questions 15 – 17, determine whether each statement is true of false.
15. If B is between M and T, MB = BT – MT. ________
1
16. If C is the midpoint of AT , then CT = TA. ________
2
17. Every segment has only one bisector. _______
18. If m1  4  m2 , find m2 . _______
1
2
A
2
19. Find mABC if BD bisects ABC , m1  5 x  11 and m2  3x  5.
D
1
B
For questions 20 – 23, refer to the figure at the right.
20. Name two right angles. __________ ___________
21. Name two supplementary angles. . __________ ___________
22. Name two congruent angles that are not right angles. . _____ ______
23. Name the obtuse angle. . __________ ___________
___________
C
A
116 
25 
65

B

39 
25
D
C
24. The measure of an angle is three times the measure of its supplement. Find the measure of the angle. _____
25. Find the value of y. ________
2y+20
3y+10 
A
2
26. Find m2 if mABC  75 and m1  16. ___________________
Geometry Mid-Term Review 2006 – 2007
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B
1
C
27. Find the value of x if if mABC  6x , m1  2 x  5, and m2  3x 1. ____________
Chapter 2
For questions 1 - 3, determine if the conclusion is true or false based on the given information.
ABD and CBD are adjacent angles.
1. Given:
_________________________________
BC and BA are opposite rays.
Conjecture: ABD and CBD are supplements.
PQ  PR .
Given:
Conjecture: RPQ is a right angle.
_________________________________
3. Given:
J, K and L are collinear.
Conjecture: JK + KL = JL.
_________________________________
2.
For questions 4 - 6, write the statement in if-then form. Underline the hypothesis once, conclusion twice.
4. Two lines intersect exactly one point. _____________________________________________________________
5. All tigers are cats. _____________________________________________________________________________
6. All right angles measure 90 degrees. ______________________________________________________________
Write the converse, inverse and contrapositive of the conditional statement.
7. Vertical angles are congruent. ___________________________________________________________________
Converse:______________________________________________________________________________
Inverse:________________________________________________________________________________
Contrapositive:__________________________________________________________________________
Complete the following statements.
8. A plane contains _______________________________________________________________________.
9. A line contains _______________________________________________________________________.
If possible, write the conclusion. State the law of logic that you used, or write “no conclusion”.
10. a) If you have a driver’s license, then you may drive a car.
b) Cindy has a driver’s license.
c)__________________________________________________________________________________________
11. a) If AB  CD , then CD  AB .
b) If CD  AB , then CD = AB.
c)_________________________________________________________________________________________
12. a) All right angles are congruent.
b) Vertical angles are congruent.
c)_________________________________________________________________________________________
For questions 13 – 15, name the property of equality that justifies each statement.
13. If mA  mB  180 and mA  110 , then 110  mB  180 . _________________________________________
14. If AB = CD, then CD = AB. ___________________________________________________________
1
15. If mK  mL , then 2mK  mL .____________________________________________________________
2
16. In the conditional “If p, then q”, the q is called the _____________________.
Geometry Mid-Term Review 2006 – 2007

3x+6
1
5x-18

5
17. Find the measure of 1 .
_____________________P
Chapter 3
1. How many pairs of skew lines does the figure at the right have? ____________
A
B
D
C
Refer to the figure below. State the transversal that forms each pair of angles. Then identify the special angle
pair name.
I
l
4
B
3
m
2. 5 and 7 __________________________
2
3. 1 and 8 __________________________
4. 4 and 10 _________________________
7
8
1
6
5. 1 and 3 __________________________
A
C
9
11
10
6. 4 and 9 __________________________
7. If m1  80 , m2  40 , and l m , find the angle measures.
m11  _____.
m3  _____, m4  _____, m5  _____, m6  _____, m7  _____, m8  _____, m9  _____, m10  _____,
5
Find the value of x and y.
8. l m
y-1 35
l
________ _________
9.
42
3y+2
3x+1
________ ________
m
Find the value of x so that p q .
10.
________
x-5
11.
28
________
2x+7
2x-3
103
135
12. Tell whether a line whose slope is undefined is horizontal, vertical or neither. _______________________
13. Find the slope of the line passing through (-3, 0) and (2, -1). __________________
14. Find the slope of a line parallel to the line passing through (5, -3) and (8, 2). __________________
15. Find the slope of the line perpendicular to the line passing through (4, -3) and (1, -1). ____________________
16. Write the equation of the line with a slope of 4 passing through (-1, 3). _________________
17. Write the equation of the line parallel to y 
1
x  9 passing through (-2, 3). ______________
2
18. Write the equation of the line perpendicular to y 
Geometry Mid-Term Review 2006 – 2007
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1
x  1 passing through (1, 4). _____________
3
Chapter 4
Determine whether each statement is true or false.
1. All isosceles triangles are acute. ____________
2. An acute triangle can be equilateral. ___________
3. A scalene triangle is never obtuse. __________
4. A right triangle can be isosceles. __________
Use the given conditions to classify each triangle by its sides and by its angles.
5. WHO , with mW  110, WH = WO = 5 cm. ______________ ______________
6. BAG , with mB  90, GB = 4 cm , BA = 3 cm. _______________ ______________
Find the value of x.
7.
4x-3
________________
5x
7x+9
8.
34
______________
3x+56
49
27
Write a congruence statement for the congruent triangles in each diagram.
Z
9.
_____________________
10.
Y
_______________________
M
J
R
X
K
N
L
P
Q
Determine which postulate or theorem can be used to prove the triangles congruent.
11.
_______ 12.
M
J
_________
13. ________
B
K
N
L
A
Always, sometimes or never.
13. An equilateral triangle is _______________ an isosceles triangle.
14. An isosceles triangle is __________ an equilateral triangle.
15. A triangle __________ has one obtuse angle and one right angle.
16. An equilateral triangle is _______________ an obtuse triangle.
17. An equilateral triangle is _______________ an acute triangle.
Find the value of x and y.
18.
_____
_____
C
E
70
x
y
19.
4y
_____ _____
49
20.
_____ _____
X
y
x
24
Geometry Mid-Term Review 2006 – 2007
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21. What is the vertex for ABC ? ___________
Chapter 5
1. Name the triangle for which GD is a median. _________
2. Name an altitude of
A
AGC . ______
D
3. Name a median to AG in
E
AGC . _______
F
B
4. Name a perpendicular bisector ______ to triangle _____.
G
C
5. Name an angle bisector. _______ to angle _____ .
List the sides of WXY in order from longest to shortest if the angles of WXY have the indicated measures.
6. mW  4x – 1
_____ _____ _____
mX  7x + 3
mY  3x – 4
7. mW  5x + 2
mX  6x - 5
mY  48 – 2x
_____ _____ _____
8. Two sides of a triangle are 16 and 22 centimeters in length. Determine whether 39 centimeters can be
the length of the third side?
_________
9. Two sides of a triangle are 21 and 24 centimeters in length. Determine whether 40 centimeters can be
the length of the third side?
_________
B
Write the inequality relating each pair of measures.
mPRQ _____ mPRS
10.
11.
7
R
mDBC _____ mABE
15
Q
15
12 12
7
5
A
P
S
9
4 E
C
D 6
Write an inequality to describe the possible values of x.
A
12.
13.
3x-2
Q
15
4x-8
2x+5
B
10
_____________
C
Geometry Mid-Term Review 2006 – 2007
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R
__________
12
2x-5
55
P
15
S
Part III: Multiple Choice
Choose the best answer for each question.
Chapter 1
1. Find the length of the segment with endpoints L(-1, -3) and M(-6, 9).
A. 13
B. 17
C. 5
D. 12
2. Points A, B and D
A. determine a plane
C. are contained in only plane P
B. are collinear
D. are noncoplanar points
F
C
A
P
E
D
B
3. What is the intersection of planes P and R.
A points A, D and B
B. AB
G
C. AB
D. AD
R
4. What is the measure of QT if R is between Q and T, QR = 14 and RT = 5?
A. 10
B. 11
C. 19
D. 9
5. Find the coordinates of the midpoint of the segment with endpoints D(6, 6) and E(-2, 2).
A. (3, 4)
B. (2, 4)
C. (4, 8)
D. (1, -1)
6. What are the sides of 5 ?
A. WG and WF
B. AB and WF
C. WB and WG
D. WB and WF
E
B
1 8 9
C 2
7. 5 and 6 are
A. adjacent
3
4
W
5
F
6
G
B. vertical
C. supplementary
A
D. complementary
7
8. 8 and 9 are
A. adjacent
B. vertical
C. supplementary
D. complementary
9. 1 and 2 are
A. adjacent
B. vertical
C. complementary
D. linear pair
10. 3 and 4 are
A. adjacent
B. vertical
C. linear pair
D. complementary
11. Find m1.
A. 25
C. 175
1
B. 155
D. 5
2x+15
3x+10
12. If mABD  40 and mABC  110 , find mDBC.
A. 150B. 130
C. 70
D. 80
D
A
B
C
13. Find mRSU if ST bisects RSU , m1  4x 12 and m2  2x  6.
A. 48
B. 18
Geometry Mid-Term Review 2006 – 2007
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9
1
S
T
2
U
C. 9
D. 24
Chapter 2
1. Choose the converse of “If 1  2 , then m1 = m2 .
A. If m1 = m2 , then 1  2
B. If 1  2 , then 2  1
C. If m1 = m2 , then m2 = m1 .
D. None of these
2. Identify the hypothesis of the statement “If today is Tuesday, then tomorrow is Wednesday.”
A. Today is not Tuesday
B. Today is Wednesday
C. Today is Tuesday
D. Tomorrow is Wednesday
3. Identify the if-then form of the following: All cars have four wheels.
A. If a vehicle has four wheels, then it is a car.
B. If a vehicle is a car, then it has four wheels.
C. If a vehicle is not a car, then it does not have four wheels.
D. None of these
4. Choose the statement that follows (1) and (2) by the law of detachment.
(1) Right angles are congruent.
(2)  A and  B are right angles
A. m  A = 90
B. m  B = 90
C. A  B
D. mA = mB
5. Which statement represents the law of syllogism.
A. If p  q is a true conditional and p is true, then q is true.
B. If p  q and q  r are true conditionals, then p  r is true.
C. If a, b and c are real numbers, then a(b + c) = ab + ac.
D. None of these
6. The transitive property of equality states “If a = b and b = c, then _____ “.
A. b = a
B. a = c
C. c = b
D. b = b
7.  P and Q form a linear pair and mP  62. Find mQ.
A. 62
B. 28
C. 118
Geometry Mid-Term Review 2006 – 2007
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D. 90
Chapter 3
1. Given l m and m2 = 72, find m3 .
A. 108B. 72
C. 18
D. 112
4
3
2. Given l m , m1= 9x +5 and m2 = x + 37, find the value of x.
A. 32
B. 4
C. 41
D. 39
l
1
2
5
m
3. Given m4  5x  2 and m5 = 3x + 28, find the value of x so that l m .
A. 26
B. 13
C. 67
D. 75
Chapter 4
1. A right triangle must be
A. isosceles
B. acute
C. scalene
D. either isosceles or scalene
2. Find the measures of the legs of an equilateral triangle PQR if PQ = 5x – 7 and PR = 2x + 5.
A. 39
B. 13
C. 12
D. 4
3. In ABC , what is the angle opposite AB ?
A. CA
B.  A
C.  B
D. C
4. In DEF , if DE  DF and EF is the hypotenuse, then DEF is
A. acute and scalene
B. right and scalene
C. right and isosceles
D. obtuse and isosceles
5. The measures of two angles of a triangle are 38 and 47. What is the measure of the third angle?
A. 85
B. 95
C. 133
D. 142
6. If IGH  KLJ , then H is congruent to
A. J
B. I
C. K
D.  L
7. Which of the following is not a postulate used to prove the congruence of two triangles?
A. ASA
B. SSA
C. SAS
D. SSS
8. The measure of the vertex angle of an isosceles triangle is 120. That is the measure of the base angle?
A. 60
B. 30
C. 35
D. 40
9. Name one additional pair of corresponding parts that need to be congruent in order to prove that
T
K
STP  MKO by ASA.
A. S  M
B. TP  KO
C. T  K
D. ST  MK
S
Geometry Mid-Term Review 2006 – 2007
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P M
O
C
Chapter 5
1. Identify the median of ABC .
A. CE
B. BF
C. AD
D. GH
G
F
D
2. Identify the altitude of ABC .
A. CE
B BF
C. AD
D. GH
A
H
3. In ABC , if mABF  39 and BF is an angle bisector, find mBCE.
A. 90
B. 51
C. 39
D. 12
E
B
Q
4. What is the longest side of the figure QUAD.
A. DQ
B QU
C. UA
D. DA
80
46
82
D
U
30
A
5. In EFG , mE = 6x – 8, mF  7x + 3, and mG = 3x – 7. Choose the list that shows the sides correctly
ordered from shortest to longest.
A. EF , FG , EG
B. FE , EG , GF
C. EG , GF , FE
D. GF , EG , FE
6. Determine which set of numbers can be the measures of the sides of a triangle.
A. 13, 10, 16
B. 1, 2, 3
C. 5.2, 11, 4.9
D. 208, 9, 219
7. Two sides of a triangle have lengths 15 cm and 19 cm. Which measurement can be the length of the third side?
A. 6 cm
B. 4 cm
C. 40 cm
D. 36 cm
8. If the sides of a triangle have measures 3x + 4, 6x – 1 and 8x + 2, find all possible values of x.
7
3
A. x > -1
B. x 
C. x 
D. x > 0
5
11
9. If M is the midpoint of JK , m1  m2 , JL = 10x + 2, and LK = 6x + 14, which is a possible value of x?
A. 1
K
B. 2
2
C. 3
1
D. 4
J
Geometry Mid-Term Review 2006 – 2007
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12
Properties
State the property, theorem, postulate or definition used to make the conclusion.
1. If UV = VW, then VW = UV.
___________________________________________________
2. If Q is a right angle, then mQ is 90  .
_____________________________________________
3. 2(x – 50) = 2x – 100. __________________________________________
4. If 1 and 2 are vertical angles, then 1  2 . ______________________
u
5. If t  u , then 2 is a right angle. _________________________
2
6.
A
B
C
AB + BC = AC.
7. If 1  2 , then m1  m2 .
8. A  A .
___________________
t
__________________________________________
______________________________________________________
________________________________________________________________________
9. If 2x + 4 = 17, then 2x = 13. ____________________________________________________________
10. T is the midpoint of SR , then ST  TR .
________________________________________________
11. If 1  2 and 2  3 , then 1  3 .
________________________________________________
12. If 3 and 4 are a linear pair, then they are supplementary.
13. If AB bisects CAD , then CAB  DAB .
_______________________________
___________________________________________
14. If 4 and 5 are supplementary, then m4  m5  180 . _____________________________________
15. If l m , then m1  m2  180 .
16. 3  4 , then l m .
_______________________________________________________
_____________________________________________________________
3
l
1
2
4
Geometry Mid-Term Review 2006 – 2007
m
13
Geometry Mid-Term Review 2006 – 2007
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