Conditional Statements
A rectangle has four right angles.
What is:
If a figure is a rectangle, then it has four right angles.
Write the biconditional statement:
If two angles have the same measure, then the angles are congruent.
If two angles are congruent, then the angles have the same measure.
What is:
Two angles are congruent if and only if they have the same measure.
Use the law of detachment to draw a conclusion:
An auto mechanic knows that if a car has a dead battery, the car will not start. A mechanic begins work on a car and finds the battery is dead. What conclusion can she make?
What is:
The car will not start.
Evan does not get enough sleep.
A: Evan will get enough sleep
B: Evan will not be tired.
C: Evan should get enough sleep
D: Evan will be tired.
Evan will be tired. D
What is Mt Everest
Identify the hypothesis and conclusion:
If y - 3 = 5, then y = 8
What is:
Hypothesis: y - 3 = 5
Conclusion: y = 8
Write the following definition as a biconditional statement:
If two lines are perpendicular, then they intersect to form right angles.
If two lines intersect to form right angles, then they are perpendicular.
What is:
Two lines are perpendicular if and only if they intersect to form right angles.
Use the law of syllogism to make a conclusion:
If a quadrilateral is a square, then it contains four right angles. If a quadrilateral contains four right angles, then it is a rectangle.
What is:
if a quadrilateral is a square, then it is a rectangle.
If you have a job, then you have an income. If you have an income, then you must pay taxes.
A: If you have a job, then you must pay taxes.
B: If you dont' have a job, then you don't pay taxes.
C: If you pay taxes, then you have a job.
D: If you have a job, then you don't have to pay taxes.
A
The Longest River in the world
What is the Nile
Write the sentence as a conditional:
A square has four congruent sides.
What is:
If a figure is a square, then it has 4 congruent sides.
Write the conditional and converse statements that make up the biconditional:
A line bisects a segment if and only if the line intersects the segment only at its midpoint.
What is:
If a line bisects a segment, then the line intersects the segment only at its midpiont.
If a line intersects a segment only at its midpiont, then it bisects the segment.
Use the Laws of Detachment and Syllogism to draw a conclusion:
If the circus is in town, then there are tents at the fairground.
If there are tents at the fairground, then Paul is working as a night watchman.
The circus is in town.Paul is working as a night watchman.
Which statement is a good definition?
A: Skew lines are lines that do not intersect.
B: Parallel lines are lines that do not intersect.
C: A square is a rectangle with four congruent sides.
D: Right angles are angles formed by two intersecting lines.
C
The most voluminous river in the world
What is the Amazon
Find a counterexample to show the statement is false:
If it is February, then there are only 28 days in the month.
What is:
On leap years, there are 29 days in February.
Write the biconditional statement as a conditional and its converse:
x^2 = 144 if and only if x = 12 or x = -12.
What is:
If x = 12 or x = -12, then x^2 = 144.
If x^2 = 144, then x = 12 or x = -12.
Use the Law of Detachment to draw a conclusion. If not possible, say not possible.
If a road is icy, driving conditions are hazardous.
Driving conditions are hazardous.
Which is the hypothesis of the following statement?
If 4 < k < 6, then -4 > k > -6.
A. 4 < k < 6
B. -4 > k > -6
A
The largest ocean in the world
WHat is the Pacific
Consider the conditional statement: Write the converse and determine its truth value:
If a figure is a square, then it has four sides.What is:
If a figure has four sides, then it is a square.
False, a four-sided figure could be a trapezoid or any parallelogram.
Test to see if the statement is reversible. If so, write it as a true biconditional statement:
A rectangle is a four-sided figure with at least one right angle.
What is:
no,
A figure with at lesat one right angle is not necessarily a rectangle.
Use the law of detachment and syllogism to draw a conclusion:
The Volga River is in Europe.
If a river is less than 2300 mi long, it is not one of the world's ten longest rivers.
If a river is in Europe, then it is less than 2300 mi long.
The Volga River is less than 2300 mi long.
The Volga River is not one of the world's longest rivers.
Which is the contrapositive of the statement?
If you can sing, then you can go with Sarah.
A: If You can't sing, then you can't go with Sarah.
B: If you can't go with Sarah, then you can't sing.
C: If you can go with Sarah, then you can sing.
B
The coldest spot on the globe
What is Vostok, Antarctica.