Review – Semester 1 Exam
Fall 2010-2011
Fill in the blank with the appropriate answer:
1. _______________________ is a ray 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. A quadrilateral with exactly 2 parallel sides is a __________________________.
6. The formula for the sum of all the interior angles of any polygon is __________________.
7. All exterior angles (one at each vertex) of a polygon equal ______.
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 __________________ and ___________________ slopes.
13. Parallel lines have __________________ slopes.
Describe and/or draw the following:
1. Midpoint
2. Describe the Law of Deduction and the Law of Syllogism
3. Exterior angles and Interior angles
4. Conditional statement
5. The four logic statements and their relationships (Hint: draw the box from class, include truth
values)
6. The four special segments
a.
b.
c.
d.
7. The four concurrent points
a.
b.
c.
d.
8. Parallel lines – Definition/draw how to show the distance between 2 parallel lines
9. Skew lines – Definition and drawing
10. Distance between a point and a line – Definition and drawing
11. Name five theorems that could be used to prove triangles congruent.
a.
b.
c.
d.
e.
12. Supplementary versus Complementary Angles – draw
13. Vertical Angles – draw
14. Supplementary Angles compared to Linear Pair – draw both
15. State the special angles pairs given 2 angles
a. 1, 8
c
9
2
c. 2, 10
1
d. 3, 6
e. 7, 8
10
d
b. 2, 4
4
a
11
3
5
f. 4, 6
b
6
7
16. Attributes of all parallelograms
a.
b.
c.
d.
e.
17. Attributes of all Rectangles (in addition to a-e above)
f.
g.
18. Attributes of all squares (in addition to a-g above)
h.
i.
j.
19. Attributes of all rhombi (in addition to a-e above)
k.
l.
8
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.
1. Given points P (–5, –7), and R (7, 3).
4.(Triangle ABC is shown below
What is the length of PR ?
2. What is the midpoint of the segment whose
endpoints have coordinates
(–10, 18) and (25, -30)?
What is the slope of a line perpendicular to AB ?
What is the slope of a line parallel to
AC ?
What is the slope of the median AD when D is
added to the diagram?
3. (Given:
QN bisects MQP
5. (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.
What is m1?
A. I and II only
Can you prove LMQ  PMQ ? If so by
what theorem?
B. II and III only
C. I and III only
Can you prove Q is the midpoint of LP ?
D. I, II, and III
6. Give a counterexample for the following
statement.
9. Draw a counter-example for the following
statements:
“If a right triangle’s right angle is at the origin,
then the slope of the hypotenuse must be
negative or positive.”
“If X is between A and B, then X is the midpoint
of AB”
“If ABCD is a rhombus, it is also a square.”
“A trapezoid can not have 2 right angles”
“If ABC is supplementary to CBD then they
are a linear pair”
7.
10. 3If mAXD = (5p + 10) , mAXB = (p +
25) and mBXD = (2p + 5), what is the
measure of BXD?
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 #?
8. If AEB = 7x + 5 and AEC = 3x - 7, what
is the value of x?
What is the value of CED?
11. What is the converse of the statement, “If
you are sixteen then you drive a car”?
What are the truth values of the conditional and
it’s converse?
Conditional –
Converse –
What would be the truth values for the inverse
and the contrapositive?
Inverse –
Contrapositive –
Is the statement bi-conditional?
12. Given that:
AB | | CD
mLRB = x – 12
mRSC = 3x – 16
15. Use the Law of Detachment to determine
which statement is true based on the following
2 statements:.
I. “Polygon ABCD has opposite sides parallel”
II “If opposite sides of a quadrilateral are
parallel then it must be a parallelogram”
A. ABCD is a parallelogram
B. ABCD is a rectangle
C. ABCD is a quadrilateral
Find mCSK.
D. ABCD is a polygon with equal sides.
Find mARL.
13. Write an equation of a line parallel to
y = –3x – 5
16. If EG is drawn to bisect AEB and
mAEG = 2x – 5 and mDEC = x + 65, what
is the value of x?
and passing through point (1, 3)
Write an equation of a line perpendicular to
the given line and passing through point (1, 3)
6, M)
14. 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?
17. Write an equation of a line that is
perpendicular to the line that contains the
points:
(–4, 4) and (2, –2)
18. “If you play basketball then you play in a
gym.”
20. Which of the following theorems cannot be
used to prove that two lines are parallel?
Which is the best statement regarding the
converse of this conditional statement?
A. If two lines are cut by a transversal so that a
pair of vertical angles is congruent, then the
lines are parallel.
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.
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.
21. Which of the following equations represents
a line perpendicular to the equation
5x + y = 17
19. The map below shows the location of
Sam’s house, the library, and the gas station.
A. y = –5x – 3
B. y =
1
(x) + 2
5
C. y = –
1
(x) – 2
5
D. y = 5x – 2
(G7C, 97, M)
22. Given: ABCD is an isosceles trapezoid with
AC = BD. Is ∆ABC congruent to ∆BAD? If so
by what reason?
A
B
What is the distance from Sam’s house to the
library?
Draw the altitude, LP, from the library (L) on
the graph above. What is the coordinate of
point P?
D
C
23. 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
25. “If it is the weekend, then it is not a school
day”
Write each of the following statements
Converse:
4
.
3
Inverse:
B. The slope of a perpendicular to the line
segment is 
3
.
4
C. The slope of a perpendicular to the line
segment is
Contrapositive:
3
.
4
D. The slope of a perpendicular to the line
segment is 
4
.
3
If the original statement is always true, then
which of the above statements is also always
true?
(G3A, 8, E)
(G7B, 66, H)
24. 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.
26. Given: LM || NP and LP bisects
Prove: ∆LMO  ∆PNO
L
NM
M
O
N
P