Name:_____________________
Geometry Quarter 1 Test - Study Guide.
1. Find the distance between the points (–3, –3) and (–15, –8).
2. Point S is between points R and T. P is the midpoint of
relationship between the specified segments. Find ST.
. RT = 20 and PS = 4. Draw a sketch to show the
3. Find AB and BC if BC = 7x – 13, AB = 4x + 26, B is the midpoint of
.
4. Find the coordinates of the midpoint of the segment with the given pair of endpoints: J(6, 6); K(2, –4)
5. Find the measures of
and
sketch that shows the given information.
if
bisects
6. In the figure shown, m AED = 117°. True or False:
and
°.
. The measure of
and
is
°. Draw a
are adjacent angles
7. a. Name a pair of vertical angles in the figure:
b. Name an angle supplementary to
in the figure.
8. Complete the table.
n
nth number
1
1
2
3
3
5
4
?
5
?
6
?
9. Identify the hypothesis and conclusion of the statement.
If yesterday was Saturday, then tomorrow is Monday.
10. "If
statement?
, then I will go to the game." What is the underlined portion called in this conditional
11. Is the statement true or false? Explain your reasoning.
Perpendicular lines always intersect at right angles.
12. Refer to the following statement: Two lines are perpendicular if and only if they intersect to form a right angle.
A. Is this a biconditional statement?
B. Is the statement true?
13. Write the converse of the true statement and decide whether the converse is true or false. If the converse is true,
combine it with the original statement to form a true biconditional statement. If the converse is false, state a
counterexample:
If four points are not coplanar, then they are not collinear.
14. True or False: True biconditional statements make good definitions.
15. Use the given endpoint R(4, 6) and midpoint M (7,8) of RS to find the coordinates of the other
endpoint S.
.
State the postulate indicated by the diagram.
16.
17.
18. Identify the property that makes the statement true.
If m 1 + m 2 = 25° and m 1 = 9°, then
.
19. True or False:
If two angles are complements of the same angle, then they must be equal in measure.
20.
1 and 2 are complementary, and
reasoning.
21.
what is
2 and
3 form a linear pair. If m 1 =
and
. If
? Justify your answer.
=
, what is m 3? Explain your
,
22. What is the distance from point A (1, 2) to line d with equation y = x - 3.
23. You and your friend each drew 3 points. Your 3 points lie in only 1 plane, but your friend's 3 points lie in more
than one plane. Explain how this is possible.
24. R, S, and T are collinear. S is between R and T. RS = 2w + 1, ST = w – 1, and RT = 18. Use the Segment Addition
Postulate to solve for w. Then determine the length of
25. If AB = 17 and AC = 32, find the length of
.
26.
In a class there are:




(Hint: Draw a Venn diagram.)
8 students who play football and hockey
7 students who do not play football or hockey
13 students who play hockey
19 students who play football
How many students are there in the class?
27. Find the length of
28. a. What are the approximate lengths of
and
?
b. Find the midpoint of each segment. What is true about the midpoints?
29. m SQR = (
)° and m PQR = (
Find m SQR and m PQR.
)° and m SQP = 70°.
30. Open-ended: Write three facts you observe in the figure below.
31. In the figure (not drawn to scale),
Solve for x and find
bisects
32. Which is not a possible value for y in the figure below?
a) 96
c) 141
b) 76
d) 89
°, and
°.
33. Give a counterexample to the following conjecture.
All mammals cannot fly.
34. Use inductive reasoning to find the next two numbers in each pattern.
2, 3, 5, 8, __, __
35. Decide whether inductive or deductive reasoning is used to reach the conclusion.
If you live in Nevada and are between the ages of 16 and 18, then you must take driver’s education to get your
license. Anthony lives in Nevada, is 16 years old, and has his driver’s license. Therefore, Anthony took driver’s
education.
36. Given that:
i. Tawana bought a new computer.
ii. All computers depreciate in value.
What conclusion can be logically deduced?
37. Use deductive reasoning to show that the product of two even numbers is even.
38. For each set of true statements , make a valid conclusion, if possible. If none can be made, write "no valid
conclusion."
a. If a triangle has two acute angles, then the third angle may be obtuse. Triangle ABC has two acute angles.
b. If I go to school, I'll ride the school bus. If I ride the school bus, I'll sit next to Kerry on the bus. I went to
school.
c. If a polygon is a regular, then it is convex. Polygon RSTU is convex.
39. Use symbolic notation to write the converse, inverse and contrapositive of the statement:
pq
Write a two-column proof.
40. Given:
Prove:
Statements:
bisects
41.
____Reasons:_____
Given:
are vertical angles;
form a linear pair
Prove:
are supplementary angles
Statements:
____Reasons:_____
42. Sketch an example of lines intersected by a transversal. Identify a pair of : alternate interior angles,
corresponding angles, consecutive interior angles and alternate exterior angles.
43. Is the statement true or false? Explain your reasoning.
Intersecting lines are always perpendicular.
44. Write the converse of the true statement and decide whether the converse is true or false. If the converse is true,
combine it with the original statement to form a true biconditional statement. If the converse is false, state a
counterexample:
If two lines are parallel, then they never intersect.
45. Use the figure to name a pair of: parallel lines, skew lines,
perpendicular lines, parallel planes and perpendicular planes.
46. Find m 1 in the figure below.
PQ and RS are parallel.
47. Explain the difference between the Alternate Interior angles theorem and Alternate Interior Angles Converse.
48. Given: Lines q and r are parallel.
Transversal t intersects lines q and r.
Prove:
are supplementary.
Statements:
49. In the figure below, if l and k are parallel lines, what is the value of x and y?
50. Use the given angle measures to decide whether lines a and b are parallel.
°,
°
____Reasons:_____
51. Calculate the slope of the line.
Does it matter which points are used? Why?
52. Writing: Explain the difference between a horizontal line and a vertical line in terms of slope. Give an example
of an equation for each type of line.
53. A line L1 has slope -1. State whether the line that passes through (–3, 2) and (5, 10) is parallel or perpendicular
to line L1 .
54. Decide whether Line 1 and Line 2 are parallel, perpendicular, or neither.
Line 1 passes through (10, 7) and (13, 9)
Line 2 passes through (–4, 3) and (–1, 5)
55. Find the slope of the line through the points (–1, –3) and (–1, 7).
56. Write the slope-intercept form of the equation of the line passing through the point (–2, –5) and parallel to the
line
57. Write the slope-intercept form of the equation of the line passing through the point (5, –4) and perpendicular
to the line
58. Write an equation in slope-intercept form
of the line shown.
59. Line l passes through (1, 1) and (–2, –8).
Graph the line perpendicular to l that passes
through (–2, 2).
60. Find the shortest distance between y = x – 1 and y = x + 3.
Geometry Quarter 1 Test - Study Guide.
Answer Section
1. 13 units
2. 12
3. AB = 78, BC = 78
4. (4, 1)
5.
°,
°
6. True
7. a.
b.
8. 7, 9, 11
9. hypothesis: yesterday was Saturday, conclusion: tomorrow is Monday
10. The hypothesis
11. True; definition of perpendicular lines.
12. A. yes
B. yes
13. If four points are not collinear, then they are not coplanar. - False
Counterexample: Four points may not be in the same line, but they may be in the same plane.
14. True
15. (-18, 22)
16. Through any three noncollinear points there exists exactly one plane.
17. If two points lie in a plane, then the line containing them lies in the plane.
18. Substitution Property of Equality
19. True
20.
. Since 1 and 2 are complementary, the sum of their measures is
form a linear pair, they are supplementary and the sum of their measures is
21. m
=
Property.
Property,
of Equality.
22. ≈ 2.8
and
=
and
.
. So, m 2 =
. Since
. So, m 3 =
–
2 and
=
3
.
and
are supplementary so
=
.
by the Angle Addition Postulate.
by the Transitive
by the Definition of Congruence. Using the Substitution
. Since
,
by the Division Property
23. An infinite number of planes intersect any one line so my friend's points are collinear. There is only 1 plane through
any 3 points not on the same line so my 3 points are not collinear.
24. 13
25.
15
26.
31 students
27.
28. a.
=
=
=
=
=
b. The midpoint of
=
=
=
=
11.4.
=
11.4.
. The midpoint of
=
=
. The midpoints are the same.
29. m SQR = 20° and m PQR = 50°
30. Sample answer:
1) m WVX = m YVX;
31. 7, 120°
2) m XVY
32.
m WVY;
3)
bisects
WVY.
b) 76
33. Answers will vary. For example, bats are mammals that can fly.
34. 12, 17
35. Deductive – it is based on logic and order.
36. Tawana's computer will depreciate in value.
37. Let 2x and 2y represent any two even numbers. Their product is (2x)(2y), or 4xy. Since 2 is a factor of 4 and thus of
4xy, (2x)(2y) is even.
38. a. The third angle of
may be obtuse.
b. I sat next to Kerry on the bus.
c. no valid conclusion
39. Converse: q  p ; Inverse:
40.
p  q ; Contrapositive:
q p.
41.
42. Sample Answer:
Alternate interior angles:  4 and  6;
Corresponding angles :  1 and  5;
Consecutive interior angles:  3 and  6;
Alternate exterior angles:  1 and  7.
43. False: Lines can intersect at any angle.
44. If two lines never intersect, then they are parallel. – False.
Counterexample: Two skew lines never intersect, but they are not in the same plane and therefore are not parallel.
45. Sample Answer:
Parallel lines: AB and DC ;
Skew lines: BC and GH ;
Perpendicular lines: AD and CD ;
Parallel planes: AED and BFC ;
Perpendicular planes: CDH and BCG .
46. 107 
47. Alt. Int. Angles Theorem: If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are
congruent.
Alt. Int. Angles Converse: If two lines are cut by a transversal, so the alternate interior angles are congruent, then
the lines are parallel.
48.
49.
x  y  36
51. 2;
50. No.
No - the slope ratio is the same for any two points on a line.
52. Sample answer:
A line having a slope of 0 is a horizontal line, that is, a line that crosses the y-axis and is parallel to the x-axis;
example: y = 3. A line with an undefined slope is a vertical line, that is, a line that crosses the x-axis and is parallel to
the y-axis; example: x = –2.
53. perpendicular
54. parallel
55. undefined
56. y =
57. y =
58. y =
59.
60.  2.83
Since y = x – 1 and y = x + 3 have the same slope, they are parallel. The shortest distance between parallel lines can
be found using a perpendicular line. Find the equation of a line perpendicular to y = x – 1. Find the points where the
perpendicular line intersects y = x – 1 and y = x + 3. The distance between these two points is the shortest distance
between the lines.