Unit 2 Math Vocab Geometry

Conditional Statement

A logical statement that has two parts, a hypothesis and a conclusion, written in if-the form

Biconditonal statement

when a conditional statement and its converse are both true, use "if and only if"

Conjecture

Statement based on observations

Counterexample

a specific case for which the conjecture is false

Deductive reasoning

uses facts, definitions, accepted properties and the laws of logic for form a logical argument

Inductive reasoning

uses specific examples and patterns to form a conjecture

Two point postulate

Through any two points there exists exactly one line

line-point postulate

A line contains at least two points

Line Intersection Postulate

If two lines intersect, then their intersection is exactly one point

three point postulate

Through any three noncollinear points there is exactly one plane

plane-point postulate

A plane contains at least three noncollinear points

Plane-Line 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

Addition Property of Equality

If you add the same number to each side of an equation, the two sides remain equal. (If a = b, then a + c = b + c)

Subtraction Property of Equality

If you subtract the same number from each side of an equation, the two sides remain equal. (If a = b, then a - c = b - c)

Multiplication Property of Equality

If you multiply each side of an equation by the same nonzero number, the two sides remain equal. (If a = b, then a ⋅ c = b ⋅c, c ≠ 0)

Division Property of Equality

If you divide each side of an equation by the same nonzero number, the two sides remain equal. (If a = b, then a/c = b/c, c ≠ 0)

Substitution Property of Equality

If a=b, then a can be substituted for b (or b for a) in any expression or equation

Reflexive Property (Real Numbers)

a=a

Reflexive Property (Segment Lengths)

AB = AB

Reflexive Property (Angle Measures)

m∠AB = m∠AB

Symmetric Property (Real Numbers)

if a=b, then b=a

Symmetric Property (Segment Lengths)

If AB=CD, then CD=AB

Symmetric Property (Angle Measures)

m∠A = m∠B, then m∠B = m∠A

Transitive Property (Real Numbers)

If a=b and b=c, then a=c

Transitive Property (Segment Lengths)

If AB=CD and CD=EF, then AB=EF

Transitive Property (Angle Measures)

If ∠AB = ∠CD and ∠CD = ∠EF, then ∠AB = ∠EF 

Reflexive Theorem (Properties of Segment Congruence)

For any segment AB, Segment AB is congruent Segment AB

Symmetric Theorem (Properties of Segment Congruence)

If Segment AB is congruent to Segment CD, then Segment CD is congruent to Segment AB

Transitive Theorem (Properties of Segment Congruence)

If Segment AB is congruent to Segment CD and Segment CD is congruent to Segment EF, then Segment AB is congruent to Segment AB

Reflexive Theorem (Properties of Angle Congruence)

For any angle AB, angle AB is congruent angle AB

Symmetric Theorem (Properties of Angle Congruence)

If Angle AB is congruent to Angle CD, then Angle CD is congruent to Angle AB

Transitive Theorem (Properties of Angle Congruence)

If Angle AB is congruent to Angle CD and Angle CD is congruent to Angle EF, then Angle AB is congruent to Angle AB

Congruent Supplement Theorem

If two angles are supplements of the same angle (or to congruent angles), then the angles are congruent

Congruent Complements Theorem

If two angles are complementary to the same angle (or to congruent angles), then they are congruent.

Linear Pair Postulate

If two angles form a linear pair, then they are supplementary

Vertical Angles Congruence Theorem

Vertical angles are congruent