Geom Classwork Check: 2-3 and 2-4 Practice

What is the biconditional statement given the conditional and converse statements:

Conditional: If an angle is obtuse, then the angle measures between 90 and 180 degrees

Converse: If the angle measures between 90 and 180 degrees, then the angle is obtuse.

• An angle is obtuse, so it measures between 90 and 180 degrees.

• An angle is obtuse, if and only if, the angle measures between 90 and 180 degrees.

• An angle measures between 90 and 180 degrees, so the angle is obtuse.

• An angle is not obtuse, if and only if, the angle does not measure between 90 and 180 degrees.

Write the conditional statement: p -> q

A lion is a cat that can roar.

• A lion is a cat, so it roars.

• If an animal is not a lion, then it is not a cat that can roar.

• If an animal is a lion, then it is a cat that can roar.

• A cat can roar, if and only if, it is a lion.

What is the biconditional statement ( p <-> q):

Conditional: If two lines intersect, then their intersection is at exactly one point.

Converse: If two lines intersect at exactly one point, then the two lines intersect.

• Two lines intersect, so their intersection is exactly one point.

• Two lines intersect, if and only if, the two lines intersect.

• Two lines intersect at exactly one point.

• Two lines intersect, if and only if, their intersection is at exactly one point.

Every football player at Archbishop Wood High School is a junior.

Chris is a football player. Therefore he is a junior.

• Inductive Reasoning

• Deductive Reasoning

Logan was told that 5 students failed the test.

So, he concluded that that class must be hard.

• Inductive Reasoning (patterns, opinions)

• Deductive Reasoning (fact)

Ava heard that two angles are right angles.

Therefore, the two angles are congruent.

• Inductive Reasoning (patterns, opinions)

• Deductive Reasoning (fact)

Tags

CCSS.HSG.CO.B.8

CCSS.HSG.SRT.A.2

CCSS.HSG.SRT.A.3

CCSS.HSG.SRT.C.6

Jessica and Nicolina came to class with wet hair.

Ayden concluded that it must be raining outside.

• Inductive Reasoning (patterns, opinions)

• Deductive Reasoning (fact)

Law of Syllogism:

If Liv studies for her math test, then she will make an A.

If Liv makes an A, then her parents will take her out to dinner.

• If Liv studies for her math test, then she will make an A.

• If Liv makes an A, then her parents will take her out to dinner.

• If Liv studies for her math test, then her parents will take her out to dinner.

• If Liv makes an A for her math test, then she studies for the test.

Law of Detachment:

If someone is a Pennsylvanian, then he/she is an American.

Bree is a Pennsylvanian.

• So, she is not an American.

• So, she is an American.

• So, she wishes she is an American.

• So, she is living the American dream.

If Kevin goes to the movie theatre, then he will eat popcorn.

If Kevin eats popcorn, then he will enjoy the movie.

If Kevin goes to the movie theatre, then he will enjoy the movie.

• Law of Syllogism

• Law of Detachment