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Review – Semester 1 Exam
Fall 2012-2013
Fill in the blank with the appropriate answer:
1. A/An _______________________ is a ray, segment, or line that divides an angle into 2 congruent
angles.
2. If a statement and its converse are both true the statement is said to be _____________________.
3. MP represents the _____________________ between point M and point P.
4. Planes are named by ____________________________________________________.
5. CPCTC stands for ________________________
_________ of ___________________
______________ are___________________.
6. A ________________________
__________ represents distance between a point and a line or
two parallel lines.
7. Distance between parallel lines will always be ______________________
8. The concurrent point that is equidistant from the vertices of a triangles is the _______________.
9. The concurrent point that is equidistant from the sides of a triangle is the _________________.
10. The balance point of a triangle is the ______________________. It can be divided into thirds where
______ is the distance from the point to a side and _________ is the distance from the point to a
vertex.
11. The distance from a point on an angle bisector to the sides of the angle is always
__________________.
12. Perpendicular lines have __________________
13. Parallel lines have __________________ slopes.
___________________ slopes.
Describe and/or draw the following: *give the Equation and/or Inequality if there is one*
14. Midpoint
15. Describe Deductive Reasoning and Inductive Reasoning
16. Exterior Angles and Interior Angles
17. Conditional Statement
18. The four logic statements and their relationships (Hint: draw the box from class, include truth values)
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19. List the four Special Segments
a.
b.
c.
d.
20. List the four Points of Concurrency
a.
b.
c.
d.
21. Parallel lines – Definition and drawing (How do you show the distance between 2 parallel lines?)
22. Skew Lines – Definition and drawing
23. Distance between a Point and a Line – Definition and Drawing
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24. Name 5 Theorems that are used prove Triangles Congruent.
a.
b.
c.
d.
e.
25. Supplementary Angles versus Complementary Angles – Define and Draw then
Compare/Contrast
26. Vertical Angles – Define and Draw
27. Supplementary Angles compared to Linear Pairs– Define and Draw then Compare/Contrast
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c
28. State the Special Angles Pairs given 2 angles
10
d
a. 1, 8
9
b. 2, 4
2
1
c. 2, 10
4
a
3
5
d. 3, 6
e. 7, 8
11
b
6
8
7
f. 4, 6
Word Bank
Alternate Exterior Angles
Alternate Interior Angles
Consecutive Interior Angles
Corresponding Angles
Vertical Angles
Linear Pair
Solve -- Draw pictures for every problem and mark all given information on the picture.
29. Given points P(–5, –7), and R(7, 3). What is the length of PR ?
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30. What is the midpoint of the segment whose endpoints have coordinates of
(–10, 18) and (25, -30)?
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31. Given: QN bisects MQP
What is m1?
Can you prove LMQ  PMQ ?
If so, by what theorem?
Can you prove Q is the midpoint of LP ?
If so, explain how.
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32. For which of the following is the Contrapositive true?
I) If a polygon is a square then it is a rectangle.
II) If a polygon is a rectangle then it is a square.
III) If a polygon is a rectangle then it is a parallelogram.
A. I and II only
B. II and III only
C. I and III only
D. I, II, and III
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33. Triangle ABC is shown on the graph
a) What is the slope of a line perpendicular to AB ?
b) What is the slope of a line parallel to AC ?
c) What is the slope of the median AD when D
is added to the triangle?
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34. Joey has 4 pieces of wood from which he plans to make a border for his triangular-shaped cactus
garden. The lengths of the wood borders are 8 feet, 10 feet, 12 feet and 18 feet. How many different
triangular borders can Joey make? Show all work.
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35. Based on the pattern above for the first 3 stages of a table’s growth, how many cells would be in the 45th
stage?
Make a table of values to help with this answer:
x
y
What equation would you use to determine the cells based on the stage #?
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36. If AEB = 7x + 5 and AEC = 3x - 7,
what is the value of x and CED?
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37. Draw a counter-example for the following statements:
a) “If X is between A and B, then X is the midpoint of AB”
b) “If a triangle is obtuse then the center of balance will not be inside the triangle.”
c) “An altitude will never intersect a vertex”
d) “If ABC is supplementary to CBD then they are a linear pair”
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38. If mAXD = (5p + 10) , mAXB = (p + 25) and mBXD = (2p + 5),
what is the measure of BXD
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39. What is the Converse of the statement, “If you are sixteen then you drive a car”?
a) What are the truth values for each of the values below using the statement above? T or F?
Conditional –
Converse –
Inverse –
Contrapositive –
b) Can the statement be bi-conditional? If so, why?
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40. Given: AB | | CD ; mLRB = x – 12; mRSC = 3x – 16
Find mCSK.
Find mARL.
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41. a) Write an equation of a line parallel to y = -3x – 5 and passing through the point (1, 3).
b) Write an equation of a line perpendicular to y = -3x - 5 and passing through point (1, 3).
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42. The midpoint of XY is located at the origin, and one endpoint of this segment has coordinates of
(22, 35). What are the coordinates of the other endpoint?
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43. In Geometryville, distances can only be measured along horizontal and vertical lines like the streets in
the map below (rise over run). Each city block in Geometryville is one unit long on each side. The town
council of Geometryville wants to place a special fountain so that it is the same distance from the
entrances to the Courthouse, the Library, and Euclid Park. The entrances are at the corners marked with
A, B, and C, respectively.
What intersection would be the best
location for the fountain?
A. Polygon Way and 2nd St.
B. Scalene St. and 2nd St.
C. Measurement Ave. and 1st St.
D. Angle Ave. and 3rd St.
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44. If EG is drawn to bisect AEB and mAEG = 2x – 5 and mDEC = x + 65, what is the value of x?
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45. “If you play basketball then you play in a gym.”
Which is the best statement regarding the converse of this conditional statement?
A. The converse is true, because you play in a gym.
B. The converse is false, because you could play volleyball.
C. The converse is true, because if you play in a gym then you are playing ball.
D. The converse is false, because you could be playing outside.
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46. Write an equation of a line that is perpendicular to the line that contains the points:
(–4, 4) and (2, –2)
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47. The map below shows the location of Sam’s house, the library, and the gas station.
a) What is the distance from Sam’s house to the library?
b) Draw the altitude, LP, from the library (L) on the graph.
What is the coordinate of point P?
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48. Which of the following theorems cannot be used to prove that two lines are parallel?
A. If two lines are cut by a transversal so that a pair of vertical angles is congruent, then the lines
are parallel.
B. If two lines are cut by a transversal so that a pair of alternate exterior angles is congruent, then
the lines are parallel.
C. If two lines are cut by a transversal so that a pair of corresponding angles is congruent, then the
lines are parallel.
D. If two lines are cut by a transversal so that a pair of consecutive interior angles is supplementary,
then the lines are parallel.
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49. Which of the following equations represents a line perpendicular to the equation
5x + y = 17
A. y = –5x – 3
B. y =
1
(x) + 2
5
1
5
C. y = – (x) – 2
D. y = 5x – 2
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50. AB in the coordinate plane has endpoints with coordinates A (2, 4) and B (8, 12). Which of the
following is true?
A. The slope of a perpendicular to the line segment is
4
.
3
B. The slope of a perpendicular to the line segment is 
C. The slope of a perpendicular to the line segment is
3
.
4
3
.
4
D. The slope of a perpendicular to the line segment is 
4
.
3
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51. AB in the coordinate plane has endpoints with coordinates A (2, 4) and B (8, 12). Write an equation
for the perpendicular bisector of the line segment.
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52. Determine the relationships between the measures of each of the given angles using
inequalities. Hint: < or >
A. mRWT & mRQW
B. mRSW & mWRS
C. mTWR & mWRT
D. mTRS & mSWR
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53. In XYZ, XY=3.5 and YZ=8. Which of the following could not be a measure of XZ?
a. 6
b. 11.5
c
5.5
d. 8
Explain why:
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L
M
54. Given: LM || NP and LP bisects NM
Prove: MO
NO
O
N
Statements
P
Reasons
B
C
55. Given: DBA  CBA , D  C
Prove: AB bisects DAC
D
Statements
A
Reasons
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56. In the picture shown, lines PR and ST are parallel and PR  ST . From this information it can be
shown, using 3 steps, that M is the midpoint of PT .
What is the correct order of the three steps needed to prove that M is the midpoint of PT ?
Statement F
PM  MT because they are corresponding parts of congruent triangles.
Statement G
RPM  STM and
 PRM  TSM because they are pairs of alternate interior angles.
Statement H
PRM  TSM because of the Angle-Side-Angle rule.
A. Statement F, Statement G, Statement H
B. Statement H, Statement G, Statement F
C. Statement G, Statement F, Statement H
D. Statement G, Statement H, Statement F
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