Question

1-5 additional practice conditional statements
write each sentence as a conditional.

1. a regular hexagon has exactly six congruent sides.
2. two supplementary angles form a line.

determine the truth - value of each conditional. explain your reasoning or give a counterexample.

1. if a figure has four congruent angles, then the figure is a square.
2. if the sidewalks are wet, then it has been raining.

write the negation of each part of the conditional. then write the converse, the inverse, and the contrapositive. determine the truth - value of each new statement.

1. if a figure is a square, then it is a rectangle.
2. if the game is field hockey, then the game is a team sport.
3. write a biconditional for the following conditional. determine the truth - value of the new statement. if two lines have the same slope, then they are parallel.
4. understand write the distributive property of multiplication over addition as a conditional statement.
5. apply the number of people in the united states who are at least 100 years old grew about 66% from 1980 to 2010. write that information as a conditional statement.

Explanation:

Step1: Rewrite as conditional

1. If a figure is a regular hexagon, then it has exactly six congruent sides.
2. If two angles are supplementary, then they form a line.

Step2: Determine truth - value

1. False. Counter - example: A rectangle has four congruent angles (all 90 degrees) but is not a square.
2. False. Counter - example: The sidewalks could be wet from a sprinkler.

Step3: For statement 5

Negation of "a figure is a square": A figure is not a square. Negation of "it is a rectangle": It is not a rectangle.
Converse: If a figure is a rectangle, then it is a square. False.
Inverse: If a figure is not a square, then it is not a rectangle. False.
Contrapositive: If a figure is not a rectangle, then it is not a square. True.

Step4: For statement 6

Negation of "the game is field hockey": The game is not field hockey. Negation of "the game is a team sport": The game is not a team sport.
Converse: If the game is a team sport, then the game is field hockey. False.
Inverse: If the game is not field hockey, then the game is not a team sport. False.
Contrapositive: If the game is not a team sport, then the game is not field hockey. True.

Step5: For statement 7

Biconditional: Two lines have the same slope if and only if they are parallel. False (vertical lines are parallel but have undefined slope).

Step6: For statement 8

If a is multiplied over the sum of b and c, then a(b + c)=ab+ac.

Step7: For statement 9

If a time period is from 1980 to 2010, then the number of people in the United States who are at least 100 years old grew about 66%.

Answer:

1. If a figure is a regular hexagon, then it has exactly six congruent sides.
2. If two angles are supplementary, then they form a line.
3. False, counter - example: rectangle.
4. False, counter - example: sprinkler.
5. Negation of hypothesis: A figure is not a square. Negation of conclusion: It is not a rectangle. Converse: If a figure is a rectangle, then it is a square (False). Inverse: If a figure is not a square, then it is not a rectangle (False). Contrapositive: If a figure is not a rectangle, then it is not a square (True).
6. Negation of hypothesis: The game is not field hockey. Negation of conclusion: The game is not a team sport. Converse: If the game is a team sport, then the game is field hockey (False). Inverse: If the game is not field hockey, then the game is not a team sport (False). Contrapositive: If the game is not a team sport, then the game is not field hockey (True).
7. Two lines have the same slope if and only if they are parallel (False).
8. If a is multiplied over the sum of b and c, then a(b + c)=ab + ac.
9. If a time period is from 1980 to 2010, then the number of people in the United States who are at least 100 years old grew about 66%.