Geometry Postulates, Theorems, etc Ch 2
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Created by:
hjmdb8 on October 3, 2009
Subjects:
geometry postulates, geometry theorems
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31 terms
Terms | Definitions |
|---|---|
 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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