Unit 2 Retake

What is a counterexample for the following conjecture:

Any number that is divisible by 3 is also divisible by 6

• 18

• 21

• 12

• 24

What is the conclusion for the following conditional statement?

It is Halloween if it is October

• It is Halloween

• It is October

• If it is October then it is Halloween

• It is not October

Identify the hypothesis and conclusion of the following conditional statement.

If two lines are parallel, then corresponding angles are congruent.

• Hypothesis: Corresponding angles are congruent

  Conclusion: two lines are parallel

• Hypothesis: Corresponding angles are not congruent

  Conclusion: two lines are parallel

• Hypothesis: Two lines are parallel

  Conclusion: Corresponding angles are congruent

• Hypothesis: Two lines are not parallel

  Conclusion: Corresponding angles are congruent

Write this statement as a conditional in if-then form.

All mammals live in the water.

• If an animal is a mammal, then it does not live in the water

• If an animal lives in the water, then all mammals live in the water

• If an animal is not a mammal, then it lives in the water

• If an animal is a mammal, then it lives in the water

What is the converse of the following conditional:

If the sky is blue, then the grass is green.

• If the sky is blue, then the grass is not green.

• If the grass is green, then the sky is blue.

• If the grass is not blue, then the sky is not green.

• If the sky is not blue, then the grass is green.

Which conditional has the same truth value as its converse?

• If a figure is a square, then it has four sides.

• If an angle has a measure of 80, then it is an acute angle.

• If two lines are parallel, then alternate interior angles are congruent.

• If x=7, then |x|=7

For the following true conditional statement write the converse. If the converse is also true combine the statements as a biconditional.

If a figure has three sides, then it is a triangle.

• If a figure is a triangle then it has three sides, true; A figure is a triangle iff it has three sides.

• If a figure is a triangle then it has three sides, false.

• If a figure does not have three sides, then it is not a triangle. true; A figure does not have three sides iff if is not a triangle.

• If a figure does not have three sides, then it is not a triangle. false

Write the two conditional statements that make up the following biconditional.

It rains if and only if it is cloudy.

• If it is not cloudy, then it is not raining.

  If it is not raining, then it is not cloudy.

• If it is raining, then it is cloudy.

  If it is cloudy , then it is raining.

• It rains if and only if it is cloudy.

  It is cloudy if and only if it rains.

• It rains.

  It is cloudy

Is the following definition of an equilateral triangle reversible? If yes write a true biconditional.

An equilateral triangle has three congruent sides.

• Reverse True. A triangle is equilateral if and only if it has three congruent sides.

• Reverse True. If a triangle has three congruent sides, then it is equilateral.

• Reverse True. If a triangle is equilateral, then it has three congruent sides.

• Reverse False.

Name the property of equality that justifies this statement.

If  $p=q$  then  $p-r=q-r$  

• Subtraction property

• Addition property

• Multiplication property
  

• Division property