2.1 - 2.3 Geometry Vocab

Conditional Statement

A logical statement that has two parts a hypothesis p and a conclusion q

words: if p then q symbols: p → q

Negation

The opposite of the original statement

words: not p symbols: ~p

Inverse

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

words: if not p, then not q symbols: ~p → ~q

Converse

To write the converse of a conditional statement, exchange the hypothesis and the conclusion (flip the two)

words: if q, then p symbols: q → p

Contrapositive

To write the contrapositive of a conditional statement, first write the converse. Then negate both the hypothesis and the conclusion

words: If not q, then not p symbols: ~q → ~p

TRUE OR FALSE: A conditional statement and its contrapositive are either both true or both false

TRUE - this is also true with the converse and the inverse where both are either true or both are false

When two statements are both true or both false, they are called…?

Equivalent statements

When written in “if-then form” the hypothesis and conclusion are which parts of the statement

Hypothesis: If part

Conclusion: Then part

Perpendicular Lines

When 2 lines intersect to form a right angle. You can write “line l (cursive l)

Biconditional statement

A statement that contains “if and only if”

words: p if and only if q symbols: p <—> q

Conjecture

An unproven statement based on observations

Inductive Reasoning

When you find a pattern in specific cases and the write a conjecture for the general case

Counterexample

A specific case for which the conjecture is false

Deductive Reasoning

Uses facts, definitions accepted properties, and the laws of logic to form a logical argument

Law of Detachment

If the hypothesis of a true conditional statement is true, then the conclusion is also true

Two point postulate

Through any two points there exists exactly one line

Line point postulates

A line contains at least two points

Line intersection postulate

If two lines intersect their intersection is exactly one point

Three point postulate

Through any three noncollinear points, there exists exactly one plane

Plane point postulate

If two points lie in a plane, then the line containing them lies in the plane

Plane intersection postulate

If two planes intersect, then their intersection is a line