Geometry Postulates, Theorems, Properties, and Definitions for proofs
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27 terms
Terms | Definitions |
|---|---|
 Ruler Postulate | distance = absolute value of difference of coordinates |
| Segment Addition Postulate | If B is between A and C, then AB+BC=AC |
| Midpoint of a Segment | The point that divides the segment into two congruent segments |
| Bisector of a Segment | a line, segment, ray, or plane that intersects the segment at its midpoint |
| Angle Addition Postulate | if point B lies in the interior of <AOC then m<AOB+m<BOC=m<AOC |
| Bisector of an Angle | the ray that divides the angle into two congruent adjacent angles |
| Statment | If p then q |
| Converse | If q then p |
| Counterexample | If not q then not p |
| Inverse | If not p then not q |
| Biconditional | statement that is a combination of the converse and the statement, contains "if and only if" |
| 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 then a/c=b/c |
| Substitution Property | If a=b, then a can be substituted for b in any equation or expression |
| Reflexive Property | a=a (mirror) |
| Symmetric Property | If a=b, then b=a |
| Transitive Property | If a=b and b=c, then a=c |
| Distributive Property | a(b+c)=ab+ac |
| Midpoint Theorem | if M is the midpoint of segment AB, then AM=1/2AB and MB=1/2AB |
| Angle Bisector Theorem | If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle |
| Bisector of an Angle | the ray that divides the angle into two congruent adjacent angles |
| Complementary Angle | two angles that add up to 90 degrees |
| Supplementary Angle | When the sum of the measures of a pair of angles add up to 180° |
| Vertical Angle | either of two equal and opposite angles formed by the intersection of two straight lines |
| Perpendicular Lines | Two lines that intersect to form right angles |
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