ms cuchrane math

Angles review

100

What are adjacent angles?

Angles that are next to each other and share a common side

200

What is the difference between supplementary and complementary angles?

Supplementary angles add up to 180 degrees and complementary angles add up to 90 degrees

300

What are vertical angles?

Angles directly across from each other on intersecting lines / on opposite sides of a vertex

400

Name all angle classifications and what they mean

Acute - less than 90 degrees

Obtuse - greater than 90 degrees

Right - equal to 90 degrees

Straight - equal to 180 degrees

500

What are all of the components of a linear pair?

1) Adjacent

2) Supplementary

3) Form a straight line

Definitions

100

What is inductive reasoning?

Making a conclusion based on observations and patterns.

200

What is a compound statement?

Two or more statements joined by the words "and" or "or"

300

What is an inverse?

Negating the hypothesis and conclusion

400

What is a conjecture?

A concluding statement reached using inductive reasoning.

500

What is a biconditional statement?

The conjunction of the conditional and the converse.

Symbolic Notations

100

What is the symbolic notation of a conjunction?

p V q

200

What is the symbolic notation of a biconditional?

p <-> q

300

What is the symbolic notation of a converse?

q -> p

400

What is this the symbolic notation of?

~p -> ~q

Inverse

500

What is this the symbolic notation of?

~q -> ~p

Contrapositive

Statements

100

What is the hypothesis of the following statement?

If you live in Nashville, then you live in Tennessee.

You live in Nashville

200

When are biconditionals true?

Both the conditional and converse are true

300

What is the inverse of the following statement?

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

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

400

Use the following statements to write a converse.

p: two angles form a linear pair

q: they are adjacent angles

If two angles are adjacent, then they form a linear pair.

500

Determine the truth value of the following statement and explain:

Angles are congruent if and only if they are vertical angles.

False; conditional is false

Deductive Reasoning

100

Use the Law of Syllogism to give a valid conclusion.

If a number is divisible by 12, then it is divisible by 6.

If a number is divisible by 6, then it is divisible by 3.

If a number is divisible by 12, then it is divisible by 3.

200

Determine whether the conclusion following the given statements is justifed by the Law of Detachment or the Law of Syllogism. If neither, write 'invalid'

Given: If it is raining, then you must bring an umbrella.

Given: You bring an umbrella.

Conclusion: It is raining.

Invalid

300

Determine whether the conclusion following the given statements is justifed by the Law of Detachment or the Law of Syllogism. If neither, write 'invalid'

Given: If Kaylee gets at least a 95 on her final exam, then she will get an A in Geometry.

Given: Kaylee got a 98 on her final exam.

Conclusion: Kaylee got an A in Geometry.

Law of Detachment

400

What is deductive reasoning?

The process of reasoning logically and drawing conclusions from given facts or statements.

500

Use the Law of Detachment or the Law of Syllogism to reach a valid conclusion. If a valid conclusion cannot be reached, write no conclusion.

Given: If the measures of two angles in a triangle are 30^o and 60^o, then the third angle is 90^o.

Given: If a triangle has a 90^o angle, then it is a right triangle.

If the measures of two angles in a triangle are 30^o and 60^o, then it is a right triangle.