Download Geometry—First Semester

Geometry 1
Name:
Worksheet: Logic
Problems 1-13: Give the letter of the single, correct answer.
1.
2.
3.
The process of making a conjecture based on a series of observed patterns is known as
A. deductive reasoning
B. obfuscation
C. proof
D. inductive reasoning
The process of drawing logically certain conclusions by using an argument is known as
A. deductive reasoning
B. obfuscation
C. brawling
D. inductive reasoning
By interchanging the hypothesis and conclusion of a conditional statement, we form another
conditional statement that is called the
A. conclusion
4.
B. counterexample
B. proof
C. biconditional
D. counterexample
A type of statement formed by combining a conditional statement and its converse into a
single statement is called a
A. converse
6.
D. converse
A series of conditional statements which are linked together in a logical chain which leads to
a conclusion involving the initial hypothesis and the last conclusion is called a
A. hypothesis
5.
C. biconditional
B. counterexample
C. biconditional
D. hypothesis
If a definition is written as a conditional statement, then
A. it is also a postulate
B. its converse is false
C. it is also a theorem
D. its converse must also be true
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7.
The Venn diagram on the right illustrates7which
of the following conditional statements?
Flys
A. If something is a Diptera, then it is a Fly.
B. If something is a Fly then it is a Diptera.
Diptera
C. Something is a Diptera if and only if it is a
Fly.
D. Something is a Fly if and only if it is a
Diptera.
8.
For the conditional statement, “If a parallelogram is a rhombus, then its sides are congruent”,
the underlined clause is called the
A. conclusion
9.
B. counterexample
C. hypothesis
D. converse
Which of the following statements has the same exact meaning as, “if a dog has a blue
tongue, then it is a chow”?
A. All things that have blue tongues are chow dogs.
B. All blue-tongued things that are chows are dogs.
C. All chows have blue tongues.
D. All dogs with blue tongues are chows.
10.
Which of the following is the converse of the statement, “if a quadrilateral is a square, then
its four sides are congruent”?
A. If the four sides of a quadrilateral are congruent, then it is a square.
B. If a square is a quadrilateral, then its four sides are congruent.
C. If the four sides are congruent, then it is a quadrilateral square.
D. If four sides are congruent, then the square is a quadrilateral.
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11.
Suppose all of the following statements are true:
All teachers are in the library.
Everyone in the library is watching a video.
Ms. Jones is a teacher.
Mr. Roberts is watching a video.
Dr. Zand is in the library.
Then which of the following might NOT be true?
A. Ms. Jones is in the library.
B. Dr. Zand is watching a video.
C. Mr. Roberts is in the library.
D. Ms. Jones is watching a video.
Problems 12-15:
A pentagon is a 5-sided figure. A regular pentagon is a special pentagon. The following suggest
what a regular pentagon is and is not:
These pentagons are regular:
Figure A
These pentagons are not regular:
Figure B
Figure C
The following statement is true:
Figure D
Figure E
Figure F
If a pentagon is regular, then all five of its sides are congruent.
12.
Write the converse of that statement.
13.
Write the biconditional of that statement.
14.
Which of the figures above can be used as a counterexample to show the converse and
biconditional are false?
15.
Could the statement be used as a definition of “regular pentagon”? Why or why not?
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16.
The last page of this guided exploration contains a set of five circles to use in this
investigation. Remove this page now to use in connection with this question.
Each circle in the set contains points on its circumference. For each of the first FOUR
circles, draw all possible line segments that connect the points that have been placed on it.
These line segments will form a number of non-overlapping regions in the interior. For each
circle, count the number of regions in the interior of the circle. Then enter this number in the
appropriate place in the table:
No. of Points
on the Circle
No. of Non-Overlapping Regions
Formed Within the Circle by the
Line Segments
2
3
4
5
Look for a pattern in the table that you have just completed.
a. Describe in words any pattern you see for the numbers in the column labeled “No. of
Non-Overlapping Regions Formed Within the Circle by the Line Segments.”
b. Use the pattern that you described in part a to predict the number of non-overlapping
regions that will be formed from all joined line segments when 6 points are placed on the
circumference of a circle.
The fifth circle has 6 points placed on its circumference. Draw all possible line segments
connecting all of these 6 points.
c.
What is the number of different non-overlapping regions for a circle with 6 points
placed on its circumference?
d.
Is the number that you obtained in part a equal to the predicted value from your pattern
in question 2 part b?
e.
(Extra Credit) Find a formula that gives the correct number of non-overlapping regions
for a circle with n points placed on its circumference. You could search the web on this.
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