Reasoning and Proofs Test
Geometry
Name: _________________________________________
Date: _________________
General Directions: Write your final answers on the space provided. Figures are not drawn to
scale.
In questions 1-7, write T if true and F if false above the premises and conclusion, then
identify the truth value of the whole statement and write it on the space provided on the
right.
1.
2.
3.
4.
5.
6.
7.
A line has at most two points
itself.
the intersection of a line and a plane can be the line
A plane exists in three noncollinear points
and
are the same line
a point has thickness.
the supplement of an acute angle can be acute.
Three distinct points will always lie on the same line
ray.
If two lines are not parallel, then they intersect
and
and
are the same
are the same line.
The contrapositive of a conditional is logically equivalent to its converse inverse
and converse are logically equivalent.
If
then
skew lines doesn’t intersect and aren’t parallel.
In questions 8-9, identify the scenario as inductive or deductive reasoning.
8.
9.
The scalloped potatoes I took from the oven were cheesy. The enchiladas I took
from the oven were cheesy. If I take cookies from the oven, they will be cheesy.
Students who study hard get good grades. You are a student who studies hard. You
will get good grades.
10. In the sequence,
, the next number is
11. Write the correct notation for the shaded region
of the Venn Diagram.
12. Is the following argument valid or invalid?
17.
18.
19.
20.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
Question 11
In questions 13-16, use the rules of valid aregument to come to a conclusion. If no
conclusion can be reached, write no conclusion.
13.
14.
15.
16.
Answers
22.
23.
24.
25.
If a persons drives a car, then they have a license. John drives a car.
Nick wants to go to the movies on Friday or Saturday night. He did not go on Saturday night.
All men are created equal. All people who are created equal are women.
My car leaves skid marks if it brakes. I didn’t apply my brakes.
In questions 21-24, true or false.
21. Line intersects line .
22.
and are coplanar.
23. Line is in plane .
24.
and determine a plane.
Questions 17-20
25. Which of the following sets of points are contained in exactly one plane?
(More than one answer is possible)
a. three collinear points
d. a line and a point not on the line
b. two intersecting lines
e. three noncollinear points
c. two points
f. one point
Questions 21-24
Reasoning and Proofs Test
Geometry
Answers
In questions 26-35, identify the statements as
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
or
true.
Supplementary angles are adjacent to each other.
Any two points connected by more than one unique line.
Two angles of a linear pair are both obtuse angles.
The sum of the measures of two acute angles is greater than the sum of the
measures of two obtuse angles.
Two lines intersect to form vertical lines.
Tw complementary angles are adjacent.
Angles that are a linear pair are adjacent.
The complement of an obtuse angle is acute.
An angle adjacent to a right angle is also a right angle.
The supplement of an acute angle is obtuse.
In questions 36-39, solve for the indicated measure.
36. If
37. If
38. If
39. If
and
.
is the midpoint of ,
.
is the midpoint of
, find the coordinates of
and
, find
and
and
is in the interior of
and
and is equidistant from rays
and
, what is the value of ?
. If
48.
is complementary to
and
49.
and
50. If
intersect so that
and
is complementary to
.
are opposite rays intersected by
, then
.
at .
30.
31.
32.
33.
34.
35.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
Question 45
In questions 47-50, justify each statement using a property, definition, postulate or theorem.
47. If
29.
38.
Questions 36-39
45. Find the value of and .
46. Two angles are complementary and one angle
has a measure that is nine times the measure of
the other angle. What is the measure of the
larger angle?
28.
37.
40. is between and . If
and
, find .
41. If
and the supplement of
has measure 22°, find
.
42. If
and
are complementary and
and
are supplementary, then
is
a(n) __________ angle.
43.
is in the interior of
. If
and
, what is
?
44.
27.
36.
, find
, find .
26.
, then
and
are supplementary.
Reasoning and Proofs Test
Geometry
Complete the proof.
51. Given:
is the midpoint of
Prove:
Statements
Reasons
1. ______________________________________
Given
3.
______________________________________
2. ______________________________________
4.
5. ______________________________________
6.
7. ______________________________________
8.
9. ______________________________________
10.
52. Given:
Definition of congruence
Substitution
Given
______________________________________
______________________________________
Simplify
Division Property of Equality
______________________________________
is a right angle;
Prove:
1.
2.
Statements
Reasons
is a right angle.
______________________________________
3.
and
are comp.
.
5.
and
are comp.
.
4.
6.
7.
______________________________________
______________________________________
______________________________________
______________________________________
______________________________________
______________________________________
Reasoning and Proofs Test
Geometry
Write a two-column proof.
53. Given:
Prove:
;
Statements
54. Given:
Prove:
bisects
Statements
Reasons
.
Reasons