AnswersGeometryIntroduction to Logic and Euclidean Geometry

Introduction to Logic and Euclidean Geometry — Test Answers

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1
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Given that over right arrow EB bisects angle CEA , which statements must be true? Choose three correct answers.

A
m angle CEA is equal to 90 degrees
B
angle CEF is a straight angle.
C
m angle CEB is equal to 2 times open paren m angle CEA close paren
D
m angle CEF is equal to m angle CEA plus m angle BEF
E
angle AEF is a right angle.
2
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If p is false, which row represents when p vee open paren q wedge r close paren is true?

A
cap h
B
cap e
C
cap g
D
cap f
4

Which is the line shown in the figure?

A
line WZ
B
line WX
C
line XY
D
line XZ
5

How many students play both basketball and tennis?

A
32
B
4
C
8
D
36
6

Which statement is true about line h ?

A
Line h is the intersection of planes cap r and cap t .
B
Line h has points on planes cap r , cap p , and cap t .
C
Line h intersects line f at two points, cap A and cap b .
D
Line h intersects plane cap p at point cap c .
7

Which rays are part of line BE ?

A
over right arrow AB and over right arrow AF
B
over right arrow AC and over right arrow AB
C
over right arrow AC and over right arrow AE
D
over right arrow AB and over right arrow AE
8

What is the missing reason in the proof?

A
transitive property
B
definition of congruent angles
C
definition of angle bisector
D
segment addition property
9

Read the statement. Doubling the dimensions of a rectangle increases the area by a factor of 4 If p represents doubling the dimensions of a rectangle and q represents the area increasing by a factor of 4 , which are true? Choose two correct answers.

A
q rightarrow p represents the original conditional statement.
B
p rightarrow approximates q represents the contrapositive of the original conditional statement.
C
approximates p rightarrow approximates q represents the inverse of the original conditional statement.
D
p rightarrow q represents the original conditional statement.
E
approximates q rightarrow approximates p represents the converse of the original conditional statement.
10

Two lines intersecting at a right angle

A
form a ray.
B
form a line.
C
are parallel.
D
are perpendicular.
11

What is the inverse of the conditional statement? If a polygon has five angles, then it is a pentagon.

A
If a polygon has five angles, then it is not a pentagon.
B
If a polygon is not a pentagon, then it does not have five angles.
C
If a polygon is a pentagon, then it has five angles.
D
If a polygon does not have five angles, then it is not a pentagon.
13

In which diagram do angles 1 and 2 form a linear pair?

A
Image with description Two lines intersect at a point, forming four angles. Angle 1 is on the left side of the intersection, and angle 2 is on the right side of the intersection.
B
Image with description A ray extends upward and to the right from a point on a horizontal line. Angle 1 is between the left side of the horizontal line and the ray. Angle 2 is between the ray and the right side of the horizontal line.
C
Image with description A horizontal line passes through a point. Two rays extend upward from the point, one to the upper left and one to the upper right. Angle 1 is between the left side of the horizontal line and the upper-left ray. Angle 2 is between the two upward rays. Angle 3 is between the upper-right ray and the right side of the horizontal line.
D
Image with description Three rays extend from the same point. One ray extends horizontally to the left, one extends vertically downward, and one extends diagonally downward to the left. A right-angle marker is shown between the horizontal and vertical rays. Angle 1 is between the horizontal ray and the diagonal ray. Angle 2 is between the diagonal ray and the vertical ray.
14

Let p : The shape is a rhombus. Let q : The diagonals are perpendicular. Let r : The sides are congruent. Which represents "The shape is a rhombus if and only if the diagonals are perpendicular and the sides are congruent”?

A
open paren p vee q close paren times vee times r
B
p left right arrow open paren q wedge r close paren
C
p wedge open paren q wedge r close paren
D
open paren p vee q close paren left right arrow r
15

Line segment AB measures 18 units. Open image in full-screen view What is d , the distance between tick marks on the number line?

A
9 units
B
2 units
C
1 unit
D
3 units
16

A flowchart proof

A
contains a set of sentences explaining the steps needed to reach a conclusion.
B
uses a visual representation of the logical flow of steps needed to reach a conclusion.
C
contains a table with a logical series of statements and reasons that reach a conclusion.
D
uses inductive reasoning to prove a statement.
17

Which undefined geometric term is described as an infinite set of points that has length but not width?

A
distance
B
sphere
C
line
D
plane
18

What is the distance between points cap A and cap b ? Open image in full-screen view

A
negative 6 units
B
5 units
C
negative 1 units
D
6 units
19

Given: p : Angles XYZ and RST are vertical angles. q : Angles XYZ and RST are congruent. Which statement is logically equivalent to p rightarrow q ?

A
If angles XYZ and RST are not congruent, then they are not vertical angles.
B
If angles XYZ and RST are vertical angles, then they are not congruent.
C
If angles XYZ and RST are not vertical angles, then they are not congruent.
D
If angles XYZ and RST are congruent, then they are vertical angles.
20

Let p : The number is even. Let q : The number is prime. Which statement is represented by p wedge q ?

A
The number is even and prime.
B
The number is even or prime.
C
The number is even if the number is prime.
D
The number is prime if the number is even.
21

If an original conditional statement is represented using p rightarrow q , which represents the converse?

A
p rightarrow q
B
q rightarrow p
C
approximates p rightarrow approximates q
D
approximates q rightarrow approximates p
23

In the diagram, what is the measure of angle WRS ?

A
5 degrees
B
37.5 degrees
C
7.5 degrees
D
25 degrees

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