Inductive/Deductive Reasoning
The Laws of Logic
Parallel Lines and Transversals
Parallel and Perpendicular Lines
100
Write a conjecture that describes the pattern in each sequence. Then use your conjecture to find the next term in the sequence.
100
Determine whether each conclusion is valid is based on the given information. Write valid or invalid and explain your reasoning.
Given: If a figure is a square, then it has four sides.
Figure A has four sides.
Conclusion: Figure A is a square.
Invalid. The figure could be a rectangle.
100
What are two angles that classify as alternate interior angles?
<3 and <6
<5 and <4
100
Determine whether the pair of lines is parallel, perpendicular and neither.
y=-1/6x+2
y=6x+4
The slopes are NOT the same so the lines are NOT parallel.
The product of the slopes is -1 so the lines are perpendicular!
-1/6*6=-1
200
Determine whether the conclusion is based on inductive or deductive reasoning.
Samir reads in the newspaper that the new highway will be closed for construction every night from 9pm to 4am. It is 9:48pm, so he concludes that the highway will be closed.
Samir is basing his conclusion on facts, so he is using deductive reasoning.
200
Draw a valid conclusion from the given statements if possible. If not possible, write "No valid conclusion".
If you do not get enough sleep, then you will be tired.
If you are tired, then you will not do well on your test.
If you do not get enough sleep, then you will not do well on your test.
200
Given lines m and n are parallel, find the value of x.
x = 134o
200
Determine whether each pair of lines is parallel, perpendicular, or neither.
Slope of JK = -5/1
Slope of LM = -4/1
NEITHER
300
Write the converse statement. Determine the truth values of the conditional and converse. If false, find a counterexample. Write a true biconditional statement if possible.
If two lines are parallel, then they have the same slope and different y-intercepts.
Conditional: If two lines are parallel, they have the same slope and different y-intercepts.
Converse: If two lines have the same slope and different y-intercepts, then they are parallel.
Two lines are parallel if and only if they have the same slope and different y-intercepts.
300
Draw a valid conclusion from the given statements if possible. If not possible, write "No valid conclusion".
If you like musicals, then you enjoy theater productions.
If you are an actor, then you enjoy theater productions.
No valid conclusion.
300
Given lines m and n are parallel, find the value of x.
300
Determine whether line AB and line CD are parallel, perpendicular or neither.
A(5, -3) B(-1, -1)
C(5, 2) D(1, 4)
Neither