Geometry Postulates, Theorems, etc Ch 2

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hjmdb8  on October 3, 2009

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Geometry Postulates, Theorems, etc Ch 2

 Postulate 5Through any two points there exists exactly one line.
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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 Throught any three noncollinear points there exists exactly one plane.
Postulate 9 A plane contains at least three 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
Conditional Statement p->q; if p, then q (equivalent statement is Contrapositive)
Converse Statement q->p; if q, then p (equivalent statement is Inverse)
Contrapositive Statement ~q->~p; if not q, then not p, (equivalent is Conditional)
Inverse Statement ~p->~q; if not p, then not q, (equivalent is Converse)
Law of Detachment if p ➡ q is a true conditional statement and p is true, than q is true
Law of Syllogism If p ->q and q->r are ture conditional statements, then p->r is true
Algebraic Addition Property If a=b, then a+c=b+c; (add same to each side keeps equal)
Algebraic Subtraction Property if a=b, then a-c=b-c (subtract same from each side keeps equal)
Algebraic Multiplication Property If a=b, then ac=bc (multiply same to each side is =)
Algebraic Division Property If a=b, and c not= 0, then a/c-b/c (divide by same on each side is =)
Algebraic Reflexive Property a=a
Algebraic Symmetric Property a=b, then b=a
Algebraic Transitive Property If a=b and b=c, then a=c
Algebraic Substitution Property if a=b, the a can be substituted for b in any equation
Reflexive Property of Equality Segments AB=BA, Angles m<A=m<A
Symmetric Property of Equality Segment: If AB=CD, then CD=AB; Angles: m<A=m<b, then m<B=m<A
Transitive Property of Equality Segments: If AB=CD and CD=EF, then AB=EF; Angles: if m<A=m<B and m<B=m<C, then ,<A=m<C
Theorem 2.1/Properties of Segment Congruence Segment congruence is reflexive, symmetric, and transitive.
Properties of Angle Congruence Theorem 2.2: Angle congruence is reflexive, symmetric, and transitive.
Right Angle Congruence Theorem Theorem 2.3: All right angles are congruent.
Congruent Supplements Theorem Theorem 2.4: If two angles are supplementary to the same angle (or to congruent angles) then they are congruent. If m<1+m<2=180' and m<2+m<3=180;, then <1~=<3.
Congruent Complements Theorem Theorem 2.5, if two angles are complementary to the same angle (or to congruent angles) then the two angles are congruent. If m<4+m<5=90' and m<5+m<6=90', then <4~=<5.
Linear Pair Postulate Postulate 12: If two angles form a linear pair, then they are supplementary
Vertical Angles Theorem Theorem 2.6: vertical angles are congruent.

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