Geometry Conditionals and Counterexamples

2.2 Conditional statements

by Ms Scott

​Conditional Statements

​A conditional statement is an if-then statement.

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

Multiple Choice

The following is a conditional statement:

If an animal is a robin, then the animal is a bird.

• False

• True

• I don't know

​Definition

A conditional is an if-then statement.

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​The hypotheses is the part p following the if.

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​The conclusion is the part q following the then.

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​Read as:" If p, then q. " or "p implies q"

 

​For example:

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​If an animal is a robin, then the animal is a bird.

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​Hypothesis: An animal is a robin

​Conclusion: The animal is a bird

​Writing a Conditional

​How can you write the following statement as a conditional?

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​Vertical angles share a vertex.

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​1. Identify the hypothesis and the conclusion.

​ Vertical angles share a vertex.

​2. Write the conditional

​ If two angles are vertical, then they share a vertex.

FINDING THE TRUTH VALUE OF A CONDITIONAL​

Is the conditional true or false. If it is false, find a counterexample

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​1. If a woman is Hungarian, then she is European.

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​2. If a number is divisible by 3, then it is odd.

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​3. If a month has 28 days, then it is February.

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​Below are the truth values of the related statements. Equivalent statements have the same truth value.

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​Conditional: If the figure is a square, then it is a quadrilateral True

​Converse: If the figure is a quadrilateral, then it is a square. False

​Inverse: If the figure is not a square, then it is not a quadrilateral. False

​Contrapositive: If the figure is not a quadrilateral, then it is not a square True

Multiple Choice

Conditional: If Maria gets married, then the reception will be at the country club. What is this statement: If the reception is at the country club, then Maria will be getting married.

• Converse

• Inverse

• Contrapositive

• Negation

Multiple Choice

Refer to the following statement: "If a polygon is a quadrilateral, then it is a trapezoid."

What is the converse of this statement?

• If a polygon is not a quadrilateral, then it is not a trapezoid.

• If a polygon is not a trapezoid, then it is not a quadrilateral.

• If a polygon is a trapezoid, then it is a quadrilateral.

• A rectangle is also a quadrilateral.

Multiple Choice

Refer to the following statement: "If a polygon is a quadrilateral, then it is a trapezoid."

What is the inverse of this statement?

• If the polygon is not a quadrilateral, then it is not a trapezoid.

• If the polygon is not a trapezoid, then it is not a quadrilateral.

• If the polygon is a trapezoid, then it is a quadrilateral.

• A rectangle is also a quadrilateral.

Multiple Choice

Refer to the following statement: "If a polygon is a quadrilateral, then it is a trapezoid."

What is the contrapositive of this statement?

• If a polygon is a trapezoid, then it is a quadrilateral.

• If a polygon is not a quadrilateral, then it is not a trapezoid.

• If a polygon is not a trapezoid, then it is not a quadrilateral.

• A rectangle is also a quadrilateral.

Multiple Choice

Given, "If I have a Siberian Husky, then I have a dog." Identify the converse.

• If I do not have a Siberian Husky, then I do not have a dog.

• If I have a dog, then I have a Siberian Husky.

• If I do not have a dog, then I do not have a Siberian Husky.

• If I do not have a Siberian Husky, then I have a dog. 

Multiple Choice

Given, "If I have a Siberian Husky, then I have a dog." Identify the inverse.

• If I do not have a Siberian Husky, then I do not have a dog.

• If I have a dog, then I have a Siberian Husky.

• If I do not have a dog, then I do not have a Siberian Husky.

• If I do not have a Siberian Husky, then I have a dog. 

Multiple Choice

Given, "If I have a Siberian Husky, then I have a dog." Identify the contrapositive.

• If I do not have a Siberian Husky, then I do not have a dog.

• If I have a dog, then I have a Siberian Husky.

• If I do not have a dog, then I do not have a Siberian Husky.

• If I do not have a Siberian Husky, then I have a dog. 

Multiple Choice

Given, "If angles are congruent, then the measures of the angles are equal." Identify the converse.

• If the measures of the angles are equal, then the angles are congruent.

• "If angles are not congruent, then the measures of the angles are not equal."

• If the measures of the angles are not equal, then the angles are not congruent.

• If the angles are not congruent, then the measure of the angles are equal.

Multiple Choice

Given, "If angles are congruent, then the measures of the angles are equal." Identify the inverse.

• If the measures of the angles are equal, then the angles are congruent.

• "If angles are not congruent, then the measures of the angles are not equal."

• If the measures of the angles are not equal, then the angles are not congruent.

• If the angles are not congruent, then the measure of the angles are equal.

Multiple Choice

Given, "If angles are congruent, then the measures of the angles are equal." Identify the contrapositive.

• If the measures of the angles are equal, then the angles are congruent.

• If angles are not congruent, then the measures of the angles are not equal.

• If the measures of the angles are not equal, then the angles are not congruent.

• If the angles are not congruent, then the measure of the angles are equal.

Multiple Choice

Conditional: If it does not rain today, then we will have practice. What is this statement called: If it rains today, then we will not have practice.

• Converse

• Inverse

• Contrapositive

• Negation

Multiple Choice

Conditional: If Maria gets married, then the reception will be at the country club. What is this statement: If the reception is at the country club, then Maria will be getting married.

• Converse

• Inverse

• Contrapositive

• Negation

Multiple Choice

Original: If Emily is not late to class, then she will not be marked tardy. What is this? If Emily is late to class, then she will be marked tardy.

• Converse

• Inverse

• Contrapositive

• Negation

Multiple Choice

Original: If Jenny buys a guitar, then she will not buy a keyboard. What is this? If Jenny does buy a keyboard, then she will not buy a guitar.

• Converse

• Inverse

• Contrapositive

• Negation