ALL FIGURES ARE NOT DRAWN TO SCALE
Name: Block: Date:
2015 - 2016 Geometry Mid-Year Quiz Review Packet
Due:1/13/16 (A Day Classes)
1/14/16 (B Day Classes)
The mid-year review quiz will be on Chapters 1 through 6 that we cover in class. The BEST way to study for the quiz will be to complete this packet, review old tests and quizzes, and look over you notes.
The review packet will be graded on:
Completion (10 points) – On January 13thand 14ththis packet will be collected in class for a completion grade. Completion means every problem has been attempted to the best of your ability and work has been shown. Late packets will be assessed a penalty.
Accuracy (10 points) -- On January 20th and 21st, we will have a 10 point quiz on problems from this packet. I will randomly select 5 problems to grade on accuracy. You will be able to use your packet on this quiz.
Completion
GOOD LUCK!!!
Chapter 1: Essentials of Geometry
1.Use the Segment Addition Postulate to solve for p.
FE = 5p – 6
EG = 3p + 20
FG = 110
2.Find the distance between A(6, 0) and B(4, 4). Keep your answer in radical form.
3.Find the midpoint of A(6, 0) and B(4, 4).
4.M is the midpoint of segment AB. Given the coordinates of A(2, 4) and M(4, 6), find thecoordinates of B.
5.Given that mGED = 61, mGEF = 3x + 8 and mDEF = 8x – 2, find mDEF.
6.In the diagram, bisects ABC. Find mABC.
7.In the figure below, mAED = 128. Which of the following statements is false?
A]mBEC = 128
B] AEB and DEC are congruent
C] BEC and CED are vertical angles
D] mAEB = 52
8.1 and 2 are supplementary angles and 1 and 3 are vertical angles. If m2 = 72, find m3.
9. Solve for x.
10. Solve for x.
For questions #11 – 13, use the diagram to the right.
11.Name all anglesthat are adjacent to BOC.
12.Name an angle that is complementary to COD.
13.Name all anglesthat are supplementary to EOA.
14.Which of the following statements is false?
A]Three non-collinear points determine a plane.
B]Any three points lie on a distinct line.
C]A line contains at least two points.
D]Through any two distinct points there exists exactly one line.
15.In the figure, mCAD is twice mCAB. What is mCAB?
Chapter 2: Reasoning and Proof
16.Rewrite the statement in if-then form: “Vertical angles are congruent.”
17.What is the converse of the statement, “If it rains, then I carry my umbrella?”
18.What is the inverse of the statement, “If two lines are parallel, then they do not intersect?”
19.What is the contrapositive of the statement, “If I like school, then I attend every day?”
20.State a counter-example to the following statement:“If x2 = 25, then x = 5.”
For questions #21 – 23, decide if a conclusion can be reached. If so, write the conclusion. If a conclusion cannot be reached, then state INVALID.
21.If you get a hit, then your baseball team will win. You hit a home run.
22.If it is July 4th, then we will have a picnic. If we have a picnic, then we will have fireworks.
23.All Redskins fans are energetic. Dave is energetic.
24.tp25. r q26.p f
pq sf
27.Let a represent “x is an odd number”.Let b represent “x is a multiple of 3”.
If x = 7, which of the following is true?
ALL FIGURES ARE NOT DRAWN TO SCALE
A]ab
B] a ~b
C] ~ab
D] ~a ~b
ALL FIGURES ARE NOT DRAWN TO SCALE
28.According to the Venn diagram, which is true?
A]All football players play offense and defense.
B] No football players play offense and defense.
C] All football players play defense.
D] Some football players play offense and defense.
Chapter 3: Parallel and Perpendicular Lines
For questions #29 – 33, line l and line m are parallel in the diagram below. Match each statement with its correct postulate or theorem.
_____ 29.2 ≅8A. Alternate interior s
_____ 30. 4 ≅6B.Corresponding s
_____ 31. 2 ≅6C.Consecutive exteriors
_____ 32.4 supp5D. Consecutive interior s
_____ 33.2supp7E.Alternate exterior s
34.Find m1, given that // .
35.In the figure,l // nand r is a transversal. Which of the following is not necessarily true?
A]2 6
B]8 2
C]7 4
D]5 3
36.In the figure shown, // and mABC = 108. Which of the following statements is false?
A]mDEF = 72
B]ABH and AEG are alternate exterior angles
C]HBF and AED are alternate interior angles
D]mGEF = 108
37.Find the slope of the line passing through the points (1, 6) and (6, 5).
38.Find the equation of a line which contains the point (2, 5) and is parallel to the line y = 3x + 5.
39.Find the equation of a line which contains the point (4, -5) and is perpendicular to the line
y = 2x + 3.
40.Are the following two lines parallel, perpendicular or neither?
-7x + 6y = 4 and 6x + 7y = 0
41. Line m contains points (1, 3) and (2, 2). Which of the following pairs of points define a line parallel to m?
A](0, 0) and (1, 1)
B] (0, 0) and (1, 5)
C] (1, 1) and (6, 2)
D] (4, 0) and (5, 5)
42.A construction worker needs to make sure a ceiling beam is parallel to its corresponding floorbeam. Using the drawing as a guide, which pair of measurements is sufficient to show the beamare parallel?
A]x = z
B]y = w
C]x = y
D]y = z
43.What value of x will make lines l and m parallel?
44.Using the information from the diagram, which is true?
A] //B]//
C] // D] //
45.Line l intersects lines w, x, y, and z. Which two lines are parallel?
Chapter 4: Congruent Triangles
46.Classify NOP by its sides.
47.Name an obtuse triangle in the diagram below.
48.The figure has angle measures as shown. What is mBCD?
49.Solve for x.
50.Find the measure of ABC.
51.ABC is a right triangle with right angle at C. Which are the possible measures of A and B? Select all that apply
A]40 and 50
B]38 and 32
C]52 and 38
D]52 and 128
52.Which figures appear to be congruent?
53.If ABCXYZ, then ______.
54.If ABCDEF, AB = 10 feet, mB = 59, and mF = 21, which of the following statementsis false?
A]AC = DF
B]BC = EF
C] mD = 100
D] BD
55.In the diagram, BE and CF. Find the value of x.
56.Which of the following statements must be true, if ADBC and AB = AC?
A]ABDACD by SSS
B]ABDACD by SAS
C]ABDACD by HL
D]There are no congruent triangles
57.If HI = JK and IJ = LK, prove the two triangles congruent and state the method.
58.Given: BE and CF. What other piece of information is needed to show that ABCDEF by ASA? Hint: Draw a diagram!
59.Refer to the figure below. ABC _____
60.Which postulate or theorem can be used to prove that RSTVUT?
61.Which postulate or theorem can be used to prove thatABCEDC?
62.Given thatand, which postulate or theorem could be used to prove that DCACDB?
63.Find the value of x and y.
64.Find the values of x and y.
65.In ABC,, which term does not describe the triangle?
A]Equilateral
B]Isosceles
C]Acute
D]Obtuse
Chapter 6: Similarity
66.Solve for a:
67.At the same time of day, a man who is 75 inches tall casts a 52.5-inch shadow and his son casts a 35-inch shadow. Determine the height of the man’s son.
For questions #68 – 70, identify the similarity postulate or theorem used to prove that ∆ABC ∆XYZ. Sketch pictures if necessary. Also, state the scale factor, if possible.
68.The side lengths of ABC are 3, 4, 6, and the side lengths of XYZare 9, 12, 18.
69.In ABC,mA = 15 and mB = 80. In XYZ,mY = 80 and mZ = 85.
70.In ABC,mB = 60and AB = 6, and BC = 12. In XYZ,mY = 60and XY = 12, and YZ = 24.
For question #70 use the diagram to the right. Round to the nearest tenth.
70.a)Length of GB.
b) Length of FC.
c) Length of BC.
d)Length of CD.
Chapter 5: Triangle Inequality
71.The longest side in the figure is .
72.Two sides of a triangle have lengths 12 and 27. The length of the third side must be greater than _____ and less then _____.
73.On the shores of a river, surveyors marked locations A, B, and C. mACB = 70 and mABC = 65. List the distances between these locations in order, least to greatest?
74.Which of the following could be the sides of ABC?
A]AB = 12, BC = 15 and AC = 2B]AB = 9, BC = 15, AC = 4
C]AB = 150, BC = 100, AC = 50D]AB = 10, BC = 8, AC = 12
75.Three lookout towers are located at points A, B, and C on a section of the national forest shown inthe diagram. Which of the following is true concerning ABC formed by the towers?
A]mA is greatest
B]mC is greatest
C]mA is least
D]mC is least