Download Assignment 2F Deductive Reasoning, Chain Rule Period ______ Date

Geometry
Assignment 2F Deductive Reasoning, Chain Rule
and Valid Conclusions
For problems 1 – 5, state whether the
given argument is valid or invalid. If it is
invalid, briefly explain why and provide a
counter example.
Name _____________________________
Period ________ Date _______________
Use the Law of Syllogism (Chain Rule) to
write the conclusion that follows from the
pair of true statements in questions 6 – 7.
6.
1.
If it is raining, then my dog gets wet.
It is raining.
2.
If the stereo is on, then the volume is loud.
If the volume is loud, then the neighbors will
complain.
Therefore, my dog is wet.
Conclusion:
If m∠A = 90˚, then ∠A is not acute.
7.
∠A is not acute.
Therefore, m∠A = 90˚.
If Hailee goes to the football game, then
Emee will go to the football game.
If Emee goes to the football game, then
Toree will go to the football game.
Conclusion:
3.
If cats prowl, mice will scatter.
Mice are scattering.
Therefore, a cat is on the prowl.
8.
If the following two premises
(statements) are true, what conclusion
can you reach?
An isosceles triangle has at least
two sides with the same length.
• ∆XYZ has three sides with the
same length.
Conclusion:
•
4.
If M is the midpoint of AC,
then AM = MC
M is the midpoint of AC.
Therefore, AM = MC.
9.
5.
If two angles are supplementary,
then the angles sum to 180˚.
∠ A and ∠ B are supplementary.
Therefore, m∠A + m∠ B = 180 ˚.
Revised 8/27/2012
If the following two premises
(statements) are true, what conclusion
can you reach?
• Points Q, R, S lie within plane P.
• Points Q, S lie on line k.
Conclusion:
page 1 of 4
Printed 8/27/2012
Geometry
Assignment 2F Deductive Reasoning, Chain Rule
and Valid Conclusions
10.
If the following two premises
(statements) are true, what conclusion
can you reach?
•
•
Name _____________________________
Period ________ Date _______________
12.
1. If a number is a rational
number, then it is a real number.
A square has four sides with the
same length and four angles with
the same measure.
2. If a number is an integer, then the
number is rational.
ABCD has four sides with the
same length.
3. If a number is a whole number,
then the number is an integer.
4. If a number is a natural number,
then the number is a whole
number.
Conclusion:
11.
The statements below are out of order.
Which of the following lists the
statements in the correct logical
order?
The statements below are out of order.
1.
If a triangle is equiangular, then it
is equilateral.
2.
If a triangle is isosceles, then at
least two sides are congruent.
3.
If a triangle is equilateral, then it is
isosceles.
4.
If a triangle has at least two sides
congruent, then it is not scalene.
13.
Which of the following lists the
statements in the correct logical
order?
a.
1, 2, 3, 4
b.
3, 2, 1, 4
c.
4, 3, 2, 1
d.
2, 3, 4, 1
Use the Chain Rule to put the
following statements in order and write
a valid conclusion.
____ If a square is a quadrilateral,
then it is a polygon.
a. 2, 4, 1, 3
____ If a square is a rectangle, then it
is a parallelogram.
b. 1, 3, 2, 4
c. 3, 4, 2, 1
____ If a square is a parallelogram,
then it is a quadrilateral.
d. 4, 2, 3, 1
Conclusion:
Revised 8/27/2012
page 2 of 4
Printed 8/27/2012
Geometry
Assignment 2F Deductive Reasoning, Chain Rule
and Valid Conclusions
14.
Use the following diagram to solve for x.
Name _____________________________
Period ________ Date _______________
Use following statement: to answer
problems 18 - 24.
(3x + 2)°
If the fruit is an apple, then the
fruit grows on a tree.
(x - 6)°
15.
18.
Classify the statement as true or false.
19.
Write the converse of the given
statement.
20.
Classify the converse as true or false.
21.
Write the inverse of the given statement.
22.
Classify the inverse as true or false.
23.
Write the contrapositive of the given
statement.
24.
Classify the contrapositive as true or
false.
Use the following diagram to solve for
x and y.
y°
x°
(500 - 3x)°
16.
17.
Use the distance formula to find the
distance between points located at
(1,6) and (-3, 9). Give both an exact
and estimated answer to the nearest
tenth.
Write a counter example.
Any two lines in a plane intersect.
Revised 8/27/2012
page 3 of 4
Printed 8/27/2012
Geometry
Assignment 2F Deductive Reasoning, Chain Rule
and Valid Conclusions
25.
Which pair of angles must be
congruent?
A)
B)
C)
D)
26.
28.
What is the midpoint of AB ?
29.
One endpoint of GH is located at
( 0, −3 ) . If the midpoint of GH is
supplementary angles
complementary angles
adjacent angles
vertical angles
Which of the following best defines a
counter example?
A) a statement accepted without
proof
B) a conclusion reached using
inductive reasoning
C) an example that proves a
conjecture false
D) a statement that you prove true
27.
Name _____________________________
Period ________ Date _______________
located at ( 7,1) , what are the
coordinates of the other endpoint?
Which counterexample shows that the
given conjecture is false?
Every perfect square has exactly three
factors.
A) The factors of 2 are 1 and 2.
30.
B) The factors of 4 are 1, 2, 4.
C) The factors of 8 are 1, 2, 4, 8.
D) The factors of 16 are 1, 2, 4, 8, 16.
Revised 8/27/2012
page 4 of 4
One endpoint of GH is located at
( 2,6 ) . If the midpoint of GH is
located at ( 5,6 ) , what are the
coordinates of the other endpoint?
Printed 8/27/2012