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M2 GEOMETRY SEMESTER 1 REVIEW PACKET
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M2 GEOMETRY REVIEW FOR MIDTERM EXAM The following reference formulas will be provided on the exam:
2 2
2 1 2 1d x x y y 1 2 1 2, midpoint2 2
x x y y
A bh 1
2A bh 2A r 2C r
The following formulas will NOT be given on the exam, but you will need to know them:
sum of interior s
2 180of an -gon
nn
sum of exterior s360
of any polygon
2 1
2 1
slope = y y
x x
y mx b y k m x h
Semester 1 Vocabulary acute angle corresponding parts line of symmetry rotation acute triangle corresponding sides line segment rotational symmetry adjacent angles counterexample midpoint scalene triangle alternate exterior angles decagon n-gon segment bisector alternate interior angles degree nonagon side angle diagonal obtuse angle skew lines angle bisector distance obtuse triangle slope angle of rotation edge octagon slope-intercept form area equiangular polygon opposite rays space base equiangular triangle parallel lines sphere base angles equidistant parallel planes statement between equilateral polygon perimeter supplementary angles center of rotation equilateral triangle pentagon surface area circumference exterior perpendicular symmetry collinear exterior angle plane theorem complementary angles heptagon point translation concave hexagon point-slope form transversal conclusion hypothesis polygon triangle conditional statement included angle proof vertex angle congruent included side quadrilateral vertex of an angle congruent triangles isosceles triangle ray vertex of a polygon consecutive interior angles interior reason vertical angles contrapositive intersection reflection x-intercept converse inverse regular polygon y-intercept convex line remote interior angles coplanar linear pair right angle corresponding angles line of reflection right triangle
M2 GEOMETRY SEMESTER 1 REVIEW PACKET
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#1-11: True or false? If false, replace the underlined word or phrase to make a true sentence. 1. Two lines are perpendicular if they intersect to form a right angle. 2. Two angles are congruent if their measures have a sum of 90. 3. If two rays intersect at a common endpoint, a plane is formed. 4. A theorem is a statement that describes a fundamental relationship between the basic terms of geometry.
For #5-7, refer to the figure at right. 5. 4 and 5 are corresponding angles.
6. Given r || t, then consecutive interior angles 4 and 6 are supplementary. 7. Line p is a transversal since it intersects one or more lines in a plane at different points. 8. A triangle that is equilateral is also called a(n) acute triangle. 9. A(n) obtuse triangle has exactly one obtuse angle. 10. A reflection is a transformation that moves all points of a figure the same distance in the same direction. 11. When a figure can be folded so that the two halves match exactly, the fold is called a line of reflection. #12-17: Choose the correct term to complete each sentence. 12. Vertical angles are two (nonadjacent or collinear) angles formed by two intersecting lines. 13. The (midpoint or angle bisector) divides a line segment into two congruent segments. 14. When a linear equation is written in the form y = mx + b, m is the (transversal, slope) of the line and b is
the y-intercept. 15. (Corresponding angles, Interior angles) are located between the lines cut by a transversal. 16. An (interior or exterior) angle is formed by one side of a triangle and the extension of another side. 17. The SAS Postulate involves two corresponding sides and the (exterior angle or included angle) they form.
M2 GEOMETRY SEMESTER 1 REVIEW PACKET
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#18-30: Choose from the terms on page 1 to complete each sentence. 18. A(n) ? divides an angle into two congruent angles. 19. Two angles are ? if their measures have a sum of 180. 20. Two angles that lie in the same plane are called ? if they share a common side and a common
vertex. 21. The statement immediately following the word if is called the ____? ___ of an if-then statement. 22. The statement immediately following the word then is called the ____? of an if-then statement.
23. The equation 56 2
8y x is in ? form.
24. If two ? are cut by a transversal, then each pair of alternate interior angles is congruent. 25. A(n) ? organizes a series of statements in logical order, starting with the given statements. 26. A triangle that has one 90° angle is called a(n) ? . 27. The ASA postulate involves two corresponding angles and their corresponding ? . 28. The ? is formed by the congruent legs of an isosceles triangle. 29. A transformation representing a flip of a figure is called a(n) ? . 30. A(n) ? is a transformation that turns every point of a pre-image through a specified angle
and direction about a fixed point. #31-34: Use the figure at the right. 31. What is another name for line ? 32. Name three points on plane P. 33. Name the intersection of planes P and N. 34. Name three non-coplanar points.
M2 GEOMETRY SEMESTER 1 REVIEW PACKET
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35. If the figure at right is not necessarily drawn to scale:
a. State one thing we CAN assume from the diagram:
b. State one thing we CANNOT assume from the diagram:
36. What is the length of AB?
37. Find the length of DE if D is between points C and E, CD = 6.5 cm, and CE = 13.8 cm.
38. Write an equation and solve. Then find the length of XZ shown at right. 39. A square has a side length of 2.3 ft. What is the area of the square? Include units with your answer. 40. A circle has a circumference of 6 cm. Find the diameter of the circle. Include units with your answer. #41-43: Use the coordinate grid given at right. 41. Find the distance between A and B. Express your answer in simplest
radical form.
42. Find the coordinates of the midpoint of CD.
M2 GEOMETRY SEMESTER 1 REVIEW PACKET
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43. Find the coordinates of a point E if C is the midpoint of AE. 44. The vertices of a triangle are 0,0P , 8,6Q , and 3, 4R . What is the perimeter of this triangle?
45. Find the value of x and y in the figure at right if UV bisects TW and UV = 40. 46. Use a protractor to measure PQR . Then classify PQR as right, acute, or obtuse.
#47-48: In the figure, EA
and EB
are opposite rays, and EC
bisects FEG . 47. Find the value of x if 82m FEG , and 5 11m FEC x .
48. If 16 10m AED y , find the value of y so that ED AB . 49. Find x, y, m 1 , and m 2 in the figure at right.
M2 GEOMETRY SEMESTER 1 REVIEW PACKET
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#50-51: Use the polygons at the right. 50. Name polygon ABCDEF by its sides. Then classify it as
convex or concave and regular or not regular. 51. Find the length of each side of polygon RST. 52. Two angles, 1 and 2 , are supplementary. Angle 1 is an acute angle. What type of angle is 2 ? 53. Write an equation, and solve: The length of a rectangle is 3 more than twice its width. Find the area of the
rectangle if its perimeter is 30 cm. 54. What is the perimeter of a regular hexagon if one side is 9 cm long? 55. Find the measure of one interior angle of a regular heptagon. 56. The measure of one exterior angle of a regular polygon is 15°. How many sides does the polygon have? 57. Find the value of x in the figure at right.
58. Give a counterexample to show this statement is false: If XY = YZ, then Y is a midpoint of XZ.
M2 GEOMETRY SEMESTER 1 REVIEW PACKET
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59. Write the following statement in if-then form: All dogs have four feet. 60. Identify the hypothesis of the statement: If you live in Chicago, then you live in Illinois. 61. Write the converse of the statement: If two lines are perpendicular to the same line, then they are
parallel. 62. Write the inverse of the statement: If today is January 1, then it is New Year’s Day. 63. Write the contrapositive of the statement: If today is New Year’s Day, then school is closed. 64. Complete the proof by supplying the missing information:
If 2 7 4x , then 11
2x .
Statements Reasons 1. 2. 2 7 7 4 7x 3. 4.
5. 11
2x
1. Given 2. 3. Simplify (or substitution) 4. 5. Simplify (or substitution)
65. If 1 50m x and 2 3 20m x , find 1m .
M2 GEOMETRY SEMESTER 1 REVIEW PACKET
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66. Complete the proof.
Given: AC bisects BAD . AC bisects BCD . 1 2 Prove: 3 4 Statements Reasons
1. AC bisects BAD . AC bisects BCD. 1 2
2. ____ ____ and ____ ____ 3. 3 4
1. Given 2. 3.
#67-72: Give the reason that justifies each statement.
67. If M is the midpoint of AB, then AM MB . 68. If A B and B C , then A C . 69. If 90m A m B and 20m B , then 20 90m A . 70. If X and Y are complementary, Z and Q are complementary, and X Z , then Y Q . 71. If PR QT , then PR = QT. 72. In the diagram at right, AB + BC = AC. #73-74: Refer to the figure at right. 73. Identify the intersection of plane SVX and plane STU.
74. Name a segment skew to WY .
M2 GEOMETRY SEMESTER 1 REVIEW PACKET
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#75-79: Refer to the figure at right.
Identify each pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
75. 2 and 12 76. 3 and 5 77. 7 and 15 78. If m n , and 8 86m , find 13m . 79. Find the values of x and y if m n , 4 6 5m x , 10 5 8m x , and 9 3 10m y . #80-82: Find the slope of the line that passes through the given points. Express answers as integers or fractions in simplest form. 80. 10, 4V , 5, 5W 81. 2, 9A , 2, 15C 82. 6,14G , 3,9L
#83-85: Find the slopes of CS
and KP
, and determine whether the lines are parallel, perpendicular, or neither. 83. 1, 12 , 5, 4 , 1,9 , 6, 6C S K P
84. 5, 6 , 3, 2 , 2,10 , 1, 4C S K P
85. 6, 7 , 3, 5 , 3,3 , 9, 7C S K P
#86- 86. s #89-whic 89. 90. 91. m 92. F 93. U
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EMESTER 1 REV
10
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EMESTER 1 REV
11
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slope of any
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EMESTER 1 REV
12
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and m.
o and m a
rid. Label thi
tion of m and
Write your a
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VIEW PACKET
abel this poin
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Use a protracdegree and n
Find x, AB, B
equation for
slope of a lin
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stitution to fi
distance form
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GEOMETRY SE
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t of intersect
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y the triangle
equilateral.
EMESTER 1 REV
13
and passi
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tion of lines
tance betwee
e by its angle
VIEW PACKET
ing through
line k.
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en and P.
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M2 GEOMETRY SEMESTER 1 REVIEW PACKET
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I
WH
S
P S
T
R Q
99. Use the distance formula to find the lengths of the sides of E F G if its vertices are 3,3E , 1, 1F , and
3, 4G . Then classify the triangle by its sides.
100. Use the figure to find the measure of each numbered angle. 101. Write two different congruence statements for the triangles shown at right. ________ ________ ________ ________ #102-103: If the given postulate proves the two triangles are congruent, which additional parts of each pair of triangles should be shown congruent?
102. AAS 103. ASA
_______ ________ _______ _______
104. In the figure at right, IH bisects W IS . For each pair of triangles: (a) Are they congruent? (b) If yes, write the triangle congruency statement, and (c) give the postulate that makes them congruent.
a. Write a triangle congruence statement:
D C
B A
M2 GEOMETRY SEMESTER 1 REVIEW PACKET
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________ ________
b. Explain why these two triangles are congruent. 105. Write a two column proof.
Given: RS TS , and V is the midpoint of RT Prove: RSV TSV 106. Write a two column proof on separate paper.
Given: D F , and bisects GE DEF
Prove: DG FG
107. KLM is isosceles, and 1 2 .
a. Explain why LK P LM N .
b. Name the reason that could be used to prove LK P LM N . Choose from SSS, SAS, ASA, and AAS.
108. Find 1m .
V
R
T
S
D
E
F
G
109. 110.
111.
112.
Find the va
Write the co
Graph A B
graph the im
Graph the im
4,5X af
lue of x.
oordinates o
B C with ver
mage of A B
mage of WX
fter the trans
M2
of the image
rtices 4, 4A
B C reflected
X with 7W
slation 4x
GEOMETRY SE
of 2,5P
, 3, 2B ,
d in the y-ax
7,1 and
4, 3y .
EMESTER 1 REV
16
reflected in
and 1,C
xis.
113.
VIEW PACKET
the line y =
1 . Then
. Graph the i
1,5B af
origin.
2.
image of ABfter a rotatio
B with 3A
on of 90 abo
3,1 and
out the
114.
t
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3,1L , M
90 about ththe x-axis.
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1, 6 , and
he origin and
M2
f L′′ if LMN
3, 2N is
d then reflect
GEOMETRY SE
N with
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EMESTER 1 REV
17
115.
VIEW PACKET
. A B C wit
and 3,C
What are th
th vertices A
1 is rotated
he coordinat
4, 4A , B
d 180 about
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1, 2B ,
t the origin.
le A′B′C′?
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