2.1 Conditional Statements

​2.1 Conditional Statements

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Hypothesis and Conclusion of a Conditional

• Hypothesis follows the 'if'

• Conclusion follows the 'then'

Multiple Choice

What is this? #30

• Conditional Statement
• Inverse
• Converse
• THIS IS A GEOMETRY CLASS!!! GIVE ME NUMBERS!

Multiple Choice

Identify the hypothesis in the statement. #1

• You like the ocean

• You are a good swimmer

• If you are a good swimmer, then you like the ocean.

• You are not a good swimmer.

Multiple Choice

What is the conclusion of this conditional statement? #15

When Andy breaks his arm, he goes to the emergency room.

• Andy goes to the emergency room

• Andy breaks his arm

Multiple Choice

When can a biconditional statement be true? #44

• When the inverse and the converse are both true
• When the original statement (conditional statement) & the contrapositive are both true.
• When the converse is true.
• When the original statement (conditional statement) and the converse are both true.

Multiple Choice

Rewrite this definition as a biconditional statement: Obtuse angles are angles with measures greater than 90° and less than 180°.

• If an angle is obtuse then the angle measure is greater than 90° and less than 180°.

• An angle is obtuse if and only if the angle measure is greater than 90° and less than 180°.

• If an angle measure is greater than 90° and less than 180° , then the angle is obtuse.

• An angle is not obtuse if and only if the angle measure is not greater than 90° and less than 180°.

Negation

Multiple Choice

Write the negation of the statement "The dog is brown". #5

• The dog is black

• The dog is not brown

• The dog is not black

• Some dogs are golden

Conditional: If two segments have the same length, then they are congruent.

Converse: If two segments are congruent, then they have the same length.

Conditional: If 3 points are coplanar, then they lie on the same plane.

Converse: If 3 points lie on the same plane, then they are coplanar.

Converse: Formed by switching the hypothesis and conclusion.

• Symbolic Form: q→p

Multiple Choice

Write the converse. #7

$$q\rightarrow p$$  

• If an animal is a puppy, then it is a dog.

• If an animal is not a puppy, then it is not a dog.

• If an animal is a dog, then it is a puppy.

• If an animal is not a dog then it is not a puppy.

Multiple Choice

Given, "If I have a Siberian Husky, then I have a dog." Identify the converse. #17

• 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

Write the converse of $$If\ 3x\ =\ 15,\ then\ x\ =\ 5.\$$  #21

• $$If\ x\ \ne5,\ then\ 3x\ \ne15.$$

• $$If\ x\ =\ 5,\ then\ 2x\ =\ 10.$$  

• $$If\ \ 3x\ \ne15,\ then\ x\ne5.$$

• $$If\ x\ =\ 5,\ then\ 3x\ =\ 15.\$$  

Inverse of a Conditional Statement

The inverse of a conditional if-then statement is the negation of the hypothesis and conclusion of a conditional statement.

To negate a statement, is to give the opposite of the original statement.

Original statement: If you are a guitar player, then you are a musician.

Inverse statement: If you are not a guitar player, then you are not a musician.

Contrapositive of a Conditional Statement

The contrapositive of a conditional if-then statement is negating and reversing the hypothesis and conclusion of a conditional statement.

Ex.

Original Statement: If you are a guitar player, then you are a musician.

Contrapositive: If you are not a musician, then you are not a guitar player.

Multiple Choice

For the inverse, we _________ the hypothesis and conclusion. #32

• switch
• negate
• switch and negate

Multiple Choice

Given, "If I have a Siberian Husky, then I have a dog." Identify the inverse. #18

• 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

Write the inverse of #22

$$If\ 3x\ =\ 15,\ then\ x\ =\ 5.\$$  

• $$If\ x\ \ne5,\ then\ 3x\ \ne15.$$

• $$If\ x\ =\ 5,\ then\ 2x\ =\ 10.$$  

• $$If\ \ 3x\ \ne15,\ then\ x\ne5.$$

• $$If\ x\ =\ 5,\ then\ 3x\ =\ 15.\$$  

Contrapositive

Example:

• If it rains, we get wet.

• If we do not get wet, it does not rain.

Multiple Choice

Write the contrapositive.

$$\sim q\rightarrow\sim p$$  #9

• If an animal is a puppy, then it is a dog.

• If an animal is not a puppy, then it is not a dog.

• If an animal is a dog, then it is a puppy.

• If an animal is not a dog then it is not a puppy.

Multiple Choice

Given, "If I have a Siberian Husky, then I have a dog." Identify the contrapositive. #19

• 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

Write the contrapositive of the following statement.

"If a figure is a triangle, then the angles add to 180.

• If a figure is not a triangle, then the angles do not add to 180.

• If the angles of a figure do not add to 180, then it is not a triangle.

• If a figure has angles that add to 180, then it is a triangle.

A conditional statement is a statement that can be written in "if-then" form.

In general, a conditional statement uses the form "If p, then q".

• The first part of the conditional statement is the hypothesis. The hypothesis follows the word "if".

• The second part of the conditional statement is the conclusion. The conclusion follows the word "then".

Watch the YouTube video "Geometry Conditional Statements" by Christine Hinkley. Here's the link: https://youtu.be/zTHnMTzPEoE

• Vocabulary: conditional statement, hypothesis, conclusion, negation, converse, inverse, contrapositive, biconditional, logically equivalent.

• To write the converse of a conditional statement, simply switch the hypothesis and conclusion.

• To write the inverse of a conditional statement, negate both the hypothesis and the conclusion.

• To write the contrapositive of a conditional statement, switch and negate the hypothesis and conclusion. The contrapositive is a combination of the converse and inverse.