Conditional Statements

Conditional Statements

If/then statements

Conditional Statement

Conditional Statement: All math teachers are cool.

• Putting the conditional statement into an if/then form: If you are a math teacher, then you are cool.

• Hypothesis: you are a math teacher

• Conclusion: you are cool

Conditional Statement: Patrick Star is friends with SpongeBob.

• Putting the conditional statement into an if/then form: If you're Patrick Star, then you are friends with SpongeBob.

• Hypothesis: you're Patrick Star

• Conclusion: you are friends with SpongeBob

Multiple Choice

Identify the conclusion of the following conditional statement.

If the angles have the same measure, then they are congruent.

• they are congruent

• the angles have the same measure

Multiple Choice

Identify the hypothesis of the following conditional statement.

If today is the first day of spring, then the month is March.

• today is the first day of spring

• the month is March

Converse

Conditional Statement:  If the Bengals win tonight, then Mrs. Yingling is happy.

Converse: If Mrs. Yingling is happy, then the Bengals won tonight.

Conditional Statement: If you are a yellow sponge, then you are SpongeBob Square Pants.

Converse: If you are SpongeBob Square Pants, then you are a yellow sponge.

Multiple Choice

Select the converse of the following conditional statement:

If I study for the test, then I will get a good grade.

• If I don't study for the test, then I will not get a good grade.

• If I get a good grade, then I studied for the test.

• If I did not get a good grade, then I did not study for the test.

Multiple Choice

Which of the following is the symbolic notation for a converse statement?

• p→q

• p↔q

• ~p→~q

• q→p

Inverse

Conditional Statement: If the Bengals win tonight, then Mrs. Yingling is happy.

Inverse: If the Bengals don't win tonight, then Mrs. Yingling isn't happy.

Conditional Statement: If you are a yellow sponge, then you are SpongeBob Square Pants.

Inverse: If you are not a yellow sponge, then you are not SpongeBob Square Pants.

Multiple Choice

Select the inverse of the following conditional statement:

If I study for the test, then I will get a good grade.

• If I don't study for the test, then I will not get a good grade.

• If I did not get a good grade, then I did not study for the test.

• If I get a good grade, then I studied for the test.

Multiple Choice

Which of the following is the symbolic notation for an inverse statement?

• p→q

• p↔q

• ~p→ ~q

• q→p

Contrapositive

Conditional Statement: If the Bengals win tonight, then Mrs. Yingling is happy.

Contrapositive: If Mrs. Yingling is not happy, then the Bengals did not win tonight.

Conditional Statement: If you are a yellow sponge, then you are SpongeBob Square Pants.

Contrapositive: If you are not SpongeBob Square Pants, then you are not a yellow sponge.

Multiple Choice

Select the contrapositive of the following conditional statement.

If I study for the test, then I will get a good grade.

• If I don't study for the test, then I will not get a good grade.

• If I get a good grade, then I studied for the test.

• If I did not get a good grade, then I did not study for the test.

Multiple Choice

Which of the following is the symbolic notation for a contrapositive statement.

•  $p\rightarrow q$  

•  $p\leftrightarrow q$  

•  $\sim p\rightarrow\ \sim q$  

•  $\sim q\rightarrow\sim p$  

Biconditional Statement

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.

Multiple Choice

Conditional Statement: If a point is a midpoint, then it divides a segments into two congruent parts.

Converse: If a point divdes a segment into two congruent parts, then it is a midpoint.

Are both of these statements true or false?

• False!

• Both True!

  Biconditional statement: A point is a midpoint iff it divides a segment into two congruent parts.

Multiple Choice

Which of the following is the symbolic notation for a biconditional statement?

• $p\rightarrow q$

• $p\leftrightarrow q$

• $\sim p\rightarrow\ \sim q$

• $q\rightarrow p$

Poll

How well do you think you understand conditional statements after today's lesson?

• I got this!

• I need a little more practice.

• I'm lost.