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Geometry CP – Semester 1 Review Packet
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Geometry CP - Semester 1 Review
Name: ______________________
1. Predict the next number. a. 1, 3, 7, 13, … _____
2. In the diagram of collinear points,
AB = BC = CD, AC = 10, and BE = 32.
AB = _____
DE = _____
b. 500, 100, 20, 4, … _____
3. Suppose J is between H and K. (draw a diagram)
HJ = 4x – 7, JK = 2x – 3, and HK = 68.
x = _____
HJ = _____
JK = _____
Is J the midpoint? _____
4. Find the distance, slope, and midpoint between the points.
a. (-3, 7) and (7, 11)
b. (-1, -4) and (3, -9)
distance = _____
midpoint = _____
slope = _____
5. If mDBC = 72,
find mABD
7. mCBD = 35
mABC = 113
mABD = _____
distance = _____
midpoint = _____
slope
= _____
6. mABD = (4x - 1)
mDBC = (3x + 5)
mABC = 81
x = _______
mABD = _______
mDBC = _______
List all the acceptable names for the angle
marked with one arc.
8. PT is an angle bisector of RPS.
a. mTPS = 39
mRPT = _____
mRPS = _____
9. Use diagram below for each. .
a. m2 = 132
m3 = _____
m4 = _____
c. m1 = (3x + 32)
m3 = (5x - 12)
x = _____
m1 = _____
b. mRPT =
mTPS =
x =
mRPS =
(6x - 17)
(x + 28)
_____
_____
b.
m1 = (4x - 3)
m4 = (5x - 6)
x = _____
m3 = _____
d.
m1 = (10x - 51)
m2 = (2y)
m3 = (6x - 11)
x = _____
y = _____
10. Find the perimeter and area of each figure.
a.
b.
Perimeter = __________
Area = __________
Perimeter =
Area
__________
= __________
11. If the area of a rectangle is 84 square feet and the height is 7 feet, find the base.
12. If the area of a triangle is 48 square yards and the base is 6 yards, find the height.
13. If 4 and 5 are supplementary and m4 = 19, find m5.
14. The midpoint of a segment is (-10, -16). One endpoint is (1, -8). Find the other endpoint.
15. Two angles are complementary, and one angle has a measure that is 9 times the measure of the
other angle. What is the measure of the larger angle?
16. Use the diagram at the right.
a. If m  AFB = 68o, what is the m  EFG?
b. If m  AFB = 68o, what is the m  AFE?
c. If  GED is complementary to  DEH
and m  GED = 46o; what is the m  DEH?
d. If  FGC is supplementary to  AFB and
m  AFB = 68o; what is the m  FGC?
e. If m  EFG = 68o,  EFG   FGE, and
 FGE   GDE + 44o; what is the m  GDE?
f.
If  FEG is complementary to  GED and
 GED is complementary to  DEH, what
is m  FEG if m  DEH = 44o?
g. If m  CGD = 68o and  CGF   BFG, what
is m  AFB?
17. Write the equation of a line that passes through (5, -7) and is parallel to y = -5x + 2.
18. Find the equation of a line that passes through (5, -7) and is perpendicular to y = -5x + 2.
19. If AB  CD , find x and y.
20. If AB  CD and m  1 = 68o, find m  4.
21. Find the values of the variables in each diagram.
a.
b.
c.
d.
e.
f.
g.
h.
22. Find the value of x that makes AB || CD .
a.
b.
23. Supply the conclusion with a reason for each diagram and set of givens.
a)
GIVEN
 1 and  2 are supp.
 3 and  1 are supp.
Conclusion
Reason
b)
GIVEN
m // n
Conclusion
Reason
c)
GIVEN
7  8
Conclusion
Reason
d)
GIVEN
Conclusion
Reason
Conclusion
Reason
RS  SE
e)
GIVEN
Diagram as shown
24. Rewrite the conditional statement in if-then form.
a. Supplementary angles have a sum of 180o.
b. Freshmen and sophomores are not allowed to drive to school.
25. Identify the hypothesis and the conclusion of each statement.
a. Skew lines lie in different planes.
hypothesis:
b. I’ll go to the game, if I don’t have to work.
hypothesis:
conclusion:
conclusion
c. What is the negation of “It is sunny” ?
26. Rewrite “Vertical angles are congruent” in conditional form and its converse.
Conditional:
Converse:
Is the statement biconditional? If so, write in biconditional form. If not, give a counterexample.
27. Write a conclusion using the true statements. If no conclusion is possible, write no conclusion.
If Al eats an apple, then Betty will buy a basketball.
If Betty buys a basketball, the Charlie will eat cake.
If Charlie eats cake, then Ditka will drive in the Daytona 500.
Al is eating an Apple.
Conclusion (if any):
28. Determine if the conclusion makes sense.
If you practice, then you will remember all the lines.
If you remember all the lines, you will get selected to be in the show.
You got selected for the show; therefore you went to practice.
True or False. Reasoning:
29. Use the given to determine which statements are true:
Given:a // b
Statements:
30. Classify the triangles by angles and by sides.
a)
b)
a) 1  8
b) 1 is supp. to 3
c) 5  7
d) 6 is supp. to 7
e) 2  3
f) if t  b, then b  a
g) 5  8
h) 3 and 7 are complementary
c)
angles: ________
angles: ________
angles: ________
sides: ________
sides: ________
sides: ________
31. Find the value of x.
a)
b)
32. Solve to find the variables.
a)
b)
c)
d)
e)
f)
33. In ABC , m  A = 54o. The m  B is 6 times the m  C. Find the measure of each angle.
(Draw a diagram)
34. In BFG , m  F = 87o. The m  B is 7 times m  G. Find the measure of each angle.
(Draw a diagram)
35. In ABC , find x, and the measures of angles A, B and C. Also, classify ABC by its angles if
m  A = (5x – 10)⁰, m  B = (4x-30)⁰, m  C = 67⁰. (Draw a diagram.)
36. ABC  DEF . Solve to find x and y.
a)
b) The perimeter of ∆ABC is 41.
37. In the triangle, m  C = 60° and m  V = 59°.
Name the shortest side and the longest side.
shortest side:
longest side:
38. Given: KP is the  bisector of RQ
KP bisects RKQ
LM = 18
NQ = 15,
RP = 12
Find QR and MN.
QR = ________
MN = ________
39. The lengths of two sides of a triangle are given to be 21 meters and 17 meters long. Describe the
possible lengths of the third side.
40. The measures of two sides of a triangle are given to be 9 feet and 10 feet long. Find a length of a
segment whose measure would be too long to form a triangle with the given two measures.
41. Given: PW = 30, KD = 70, AD = 80.
find the perimeter of ΔHPW.
42. Fill each blank with <, >, or =.
a. AF _____ DL
b. WGP _____ HGP
43. Write an inequality that compares QD to QZ.
Then solve the inequality for x.(Not drawn to scale.)
44. Write an inequality using the Hinge Theorem
(or converse) describing the restriction on x.
Then, solve it for x.
45. In the diagram, HC is an angle bisector of
ΔDHL. Solve for x and find DL.
46. In the figure, TM is an altitude of ΔATJ .
Find the value of x and AT.
47. Determine whether GR is a median of
ΔNRP. Show work to justify your answer.
48. Given: AC is an altitude of ΔABE
ΔABD is equilateral
AD is a median of ΔABE
AB = 32
49. Find the coordinates of the endpoints of the
of the midsegment parallel to AC .
Find CE and m  ADE.
50. Find the value of x and list the sides of ΔABC in order from shortest to longest if:
mA  9x  29
mB  93  5x
mC  10x  2
(Draw a diagram.)
x = __________
order of sides = __________
51. Given the diagram as marked. Find x and KM.
52. F, G, and E are midpoints of the sides of ΔBMY.
If FG = 2x – 1 and BY = 5x – 7, find BE and BY.
53. Determine if each pair of triangles can be proved to be congruent. If so, state the reason.
a)
b)
c)
d)
e)
f)
MD is a median
MD is an altitude
54. What does CPCTC stand for and when is it used?
55. Give the name of any quadrilateral with the following characteristics:
a) both pairs of opposite sides parallel
b) one pair of opposite sides parallel
c) opposite sides congruent
d) opposite angles congruent
e) all right angles
f) all sides congruent
d) Quadrilateral with all sides congruent and right angles.
56. List 5 properties of PARALLELOGRAMS
1.
2.
3.
4.
5.
57. Find the value of each variable in the parallelogram.
a)
b)
57c. Find mE. (not a parallelogram)
c)
58. Find the missing lengths of the parallelogram:
JK = _____
59. Find the value of x that makes the
polygon a parallelogram.
JM = _____
MK = _____
JL = _____
60. Find the value(s) of x that will make the polygon a parallelogram.
a)
b)
61. Find the value of each variable and the missing lengths in the parallelogram.
a)
b)
x = _______
x = _______
HK _______
y = _______
Part 2. Proofs. You will need extra paper to complete most of the proofs.
1. Use coordinate geometry to verify LUKE
is a parallelogram. Show all work and
state the reason that proves the shape
is a parallelogram.
How do you know it is NOT a rectangle
based on coordinate geometry?
2. Given:  Wis a right angle
 S is a right angle
Prove:  W   S
3. Given: O is the midpoint of DG
Prove: DO  OG
4. Given:  2   3
Prove: m // n
5. Given: RS  ST
WT  ST
Prove:  S   T
6. Given:  2   3
Prove:  1   4
7. Given:  5   8
Prove:  1   4
8. Given: BC  EF
BA  ED
B  E
9. Given: C is the midpoint of BD
AB // DE
Prove: AB  ED
Prove: ABC  DEF
10. Given: ID is an altitude of isosceles ΔVKI
Prove: DV  DK
Statements
Reasons
1. ID is an alt. of isos. ΔVKI
1.
2. IDV and IDK are rt.  ’s
2.
3. IDV  IDK
3.
4. ID  ID
4.
5. V  K
5.
6. VDI  KDI
6.
7.
7.
11. Use slope to determine which lines are perpendicular. Justify your reason.
1.
a.
b.
5.
18⁰
21
4/5
2.
AB = 5
DE = 22
6.
x = 11
7. mABD= 78⁰
8a. mRPT = 39⁰
mABD= 43⁰
mRPS = 78⁰
mDBC= 38⁰, the angle can be named ABD or DBA
9a. m3 = 48⁰ b.
m4 =132
11.
12.
13.
14.
15.
23.
a.
b.
c.
d.
e.
12
16
161⁰
(-21,-24)
81⁰
x = 21
m3 =81
16a. 68⁰
b. 112⁰
c. 44⁰
d. 112⁰
e. 24⁰
f. 44⁰
g. 68⁰
3.
c.
x = 13
HJ = 45
JK = 23
x = 22
m1 =98
4a. d = 2 29
mid = (2,9)
m = 2/5
d.
17. y = -5x + 18
x = 10
y = 65.5
19. x = 9, y = 54
b.
d = 41
mid = (1,-6.5)
m = -5/4
x=9
mRPS = 74⁰
10a. P = 28
A = 40
21a.x= 110⁰
b. x = 115⁰
c. x = 90⁰
d. x = 73⁰
e. x = 60⁰
f. x = 50⁰
g. x = 45
18. y = 1/5x – 8
b.
b.
y = 110⁰
y = 115
y = 90⁰
y = 41⁰
y = 60⁰
y = 50⁰
h. x = 28.5
P = 38
A = 42.5
22a. 56
22b. 74
20. m  4 = 22⁰
Conclusion
Reason
If  ‘s are supp to the same  ,→ they are  to each other.
1 3
 5 supp  6
If // lines → same side (consecutive) interior  ’s are supplementary
m // n
If corresponding  ’s are  → // lines
S is the midpoint of RE If a point divides a segment into 2  segments → it is a midpoint
or S bisects RE
If a point divides a segment into 2  segments → it is bisected
If  ’s are vertical  ’s → 
 1   4 or
 1 and  3 are a linear pair
If  ’s are adjacent and supplementary → linear pair (assumed from diagram)
24a. If  ’s are supplementary angles, then they have a sum of 180o.
b. If a student is a freshmen or a sophomore, then they are not allowed to drive to school.
25a. h: skew lines
b. h: I don’t have to work
c: lie in different planes
c: I’ll go to the game
Negation: It is not sunny.
26. If angles are vertical angles, then they are congruent.
If angles are congruent, then they are vertical angles.
Not biconditional because the converse is not true.
27. Ditka will drive in the Daytona 500.
28. False. You may be the only person that tried out.
29. a, c, and d are true (rest are false)
30. a.
b.
c.
32a. x = 76⁰
b.
y= 23⁰, z = 132⁰
33. m  A = 54o
m  B = 108⁰
m  C = 18⁰
x = 8 or -5
c.
34. x = 11.625
35.
m  F = 87⁰
m  B = 81.375⁰
m  G = 11.625⁰
right scalene
31a.70o
obtuse isosceles
b. x = 7
equilateral equiangular
x = 48⁰
y = 84⁰
d.
x = 15
y = 40/3
x = 17
m  A = 75⁰
m  B = 38⁰
acute scalene
36a. x = 23.7
y = 17.8
38. QR = 24
MN = 18
39. 4 < x < 38
40. x > 19
41. 105
44. 3x – 3 > 21
x >8
45. x = 15
DL = 92
46. x = 8
AT = 135
47. NG =
e.
x = 16.4
b. x = 9
y=1
f.
37. short = LC
long = VC
42a. > b. >
47 and PG =
50. x = 4
51. x = 16
AB, BC, AC
KM = 184
53a. none
b. SAS
c. ASA
d. ASA or AAS
e. SAS
f. HL
55a. parallelogram, rhombus, rectangle, square
56.
b. trapezoid, isosceles trapezoid
c. parallelogram, rhombus, rectangle, square
d. parallelogram, rhombus, rectangle, square
e. rectangle, square
f. square, rhombus
g. square
59. x = 20.3
60a. x = 4 or 1
61a. x = 7.5
60b. x = 2 or 5/4
HK = 29
57a. m = 133⁰
58.
n = 47⁰
t = 78
b.x = 25, y = 24 c. 72o
JK =80
JM = 52
MK = 62
JL = 90
43. 8x – 5 > 7x + 2
x >7
73 , not =, so RG is not a median.
48. CE = 48
49. (-1,6) & (3,-1)
m  ADE = 120⁰
54. Corresponding
Parts of
Congruent
Triangles are
Congruent
x = 17
y = 122⁰
52. x = 5, BE = 9, BY = 18
opp. sides //
opp. sides 
opp.  ‘s 
consecutive ‘  s supp.
diagonals bisect each
other
61b. x = 16
y = -8
1.
Slope of LU and EK = 0/10. Same slope = parallel.
Slope of LE and UK = -10/1. Same slope = parallel.
However, slopes not opposite reciprocal, so not  .
Therefore, not a rectangle.
2.
1) W is a right angle
1) Given
2) S is a right angle
2) Given
3)  W   S
3) If 2  ’s are rt  ’s → they are 
3.
1) O is the midpt of DG 1) Given
2) DO  OG
2) If a pt. is a midpt. → it splits a segment into 2  segments
4.
1) 2  3
2) m // n
1) Given
2) If alternate interior  ’s are  → parallel lines
5.
1) RS  ST
1) Given
2) WT  ST
3) S is a rt 
4) T is a rt 
5) S  T
2) Given
3) if  lines → rt  ’s
4) same as 3
5) if  ’s are rt  ’s → 
6.
7.
1)
2)
3)
4)
1)
2)
3)
4)
2  3
1  2
3  4
1  4
5  8
 5 is supp to  1
 8 is supp to  4
1  4
1) Given
2) If  ’s are vertical  ’s → 
3) same as 2
4) transitive (if 2  ’s are  to 
 to each other)
1) Given
2) If 2  ’s form a linear pair → supp
3) same as 2
4) Supplements of   ’s are 
8.
1) BC  EF
1) Given
2) BA  ED
2) Given
3)  B   E
3) Given
4) ABC  DEF
4) SAS
9.
1) C is the midpt of BD
2) BC  CD
3) AB // ED
4) A  E
5) B  D
6) ABC  EDC
7) AB  ED
 ’s → they are
1) Given
2) If a point is a midpoint → it splits a segment into 2  segments
3) Given
4) If // lines → alternate interior angles 
5) same as 4
6) AAS
7) CPCTC
10. Reasons
1. Given
2. If a segment is an altitude then it forms right angles
3. If right angles, then congruent
4. Reflexive
5. If a triangle is isosceles, then the base angles are congruent
6. AAS
7. CPCTC
*The missing statement for #7 is DV  DK
11. Slope of AY = 8/3, slope of BD = 4/1, and slope of AB is -1/4, therefore BD  AB because they have slopes that are
opposite and reciprocal.