## Ch. 2 Geometry vocab, formulas, theorems, etc.

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# Ch. 2 Geometry vocab, formulas, theorems, etc.

 Conditional StatementA type of logical statement that has two parts, a hypothesis and a conclusion
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#### Definitions

Conditional Statement A type of logical statement that has two parts, a hypothesis and a conclusion
Hypothesis The if part of a conditional statement.
Conclusion The then part of a conditional statement
Converse of a conditional statement The statement formed by switching the hypothesis and conclusion of a conditional statement
Negation The negative of a statement.
Inverse The statement formed when you negate the hypothesis and conclusion of a conditional statement
Contrapositive The statement formed when you negate the hypothesis and conclusion of the converse of a conditional statement
Postulate 5 Through any two points there exists exactly one line.
Postulate 6 A line contains at least two points
Postulate 7 If two lines intersect, then their intersection is exactly one point
Postulate 8 Through any 3 noncollinear points there exists exactly one plane
Postulate 9 A plane contains at least 3 noncollinear points
Postulate 10 If two points lie in a plane, then the line containing them lies in the plane
Postulate 11 If two planes intersect, then their intersection is a line
Biconditional statement A statement that contains the statement if and only if.
Symbolic Notation P represents the hypothesis and Q represents the conclusion
Deductive Reasoning This uses facts, definitions, and accepted properties in a logical order to write a logical argument
Inductive Reasoning Where previous examples and patterns are used to form a conjecture
Law Of Syllogism If p-q and q-r are true conditional statements, then p-r is true.
Law of Detachment If p-q is a true conditional statement and p is true, then q is true.
Addition property of equality If a=b, then a+c=b+c
Subtraction property of equality If a=b. then a - c= b - c
Multiplication property of equality If a=b, then ac=bc
Division property of equality If a=b and c is not equal to 0, then a/c=b/c
Reflexive property of equality For any real number a, a=a
Symmetric property of equality If a=b, then b=a
Transitive property of equality If a=b and b=c, then a=c
Substitution property of equality If a=b, then a can be substituted for b in any equation or expression
Reflexive property of segment length For any segment AB, AB=AB
Reflexive property of angle measures For any angle A, m<A=m<A
Symmetric property of segment length If segment AB= segment CD, then segment CD= segment AB
Symmetric property of angle measures If m<A=m<B, then m<B=m<A
Transitive property of segment length If AB=CD and CD=EF, then AB=EF
Transitive property of angle measures If m<A=m<B and m<B=m<C, then m<A=m<C
Theorem A true statement that follows as a result of other true statements.
Reflexive property of segment congruency For any segment AB, seg. AB= seg. AB
Symmetric property of Segment congruence If seg. AB= seg. CD, then seg. CD= seg. AB
Transitive property of Segment congruence If seg. AB is congruent to seg. CD, and seg. CD is congruent to seg. EF, then seg. AB is congruent to seg. EF
Definition of Congruent Segments segment PQ is congruent to segment XY
Definition of midpoint Q is the midpoint of seg. PR
Reflexive property of angle congruence For any angle A, <A is congruent to <A
Symmetric property of angle congruence If <A is congruent to <B, then <B is congruent to <A
Transitive property of angle congruence If <A is congruent to <B and <B is congruent to <C, then <A is congruent to <C
Definition of congruent angles <A is congruent to <B
Right angle congruence theorem All right angles are congruent
Congruent supplements theorem If two angles are supplementary to the same angle or to congruent angles, then they are congruent
Congruent Complements theorem If two angles are complementary to the same angle or to congruent angles then the two angles are congruent
Linear pair postulate If two angles form a linear pair, then they are supplementary
Vertical angles theorem Vertical angles are congruent

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