Geometry Theorms, Postulates, Etc.
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Created by:
alexismccolgan on October 11, 2011
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52 terms
Terms | Definitions |
|---|---|
 right angle congruence thereom | all right angles are congruent. |
| congruent supplements thereom | if 2 angles are supplementary to the same angle or to congruent angles, then they are congruent to each other. |
| congruent complements thereom | if 2 angles are complementary to the same angle or to congruent angles, then they are congruent to each other. |
| vertical angles thereom | vertical angles are congruent. |
| theorem 3.1 | if 2 lines intersect to form a linear pair of congruent angles, then the lines are perpendicular. |
| theorem 3.2 | if 2 sides of 2 adjacent acute angles are perpendicular; then the angles are complementary. |
| theorem 3.3 | if 2 lines are perpendicular then they intersect to form 4 right angles. |
| alternate interior angles theorem | if 2 parallel lines are cut by a transversal then the pairs of consecutive interior angles are supplementary. |
| alternate exterior angles thereom | if 2 parallel lines are cut by a transversal, alternate exterior pairs are congruent. |
| perpendicular transversal theorem | if a transversal is perpendicular to one of 2 parallel lines, it is perpendicular to the other one. |
| segment bisector | is a segment, ray, line, or plane that intersects a segment at its midpoint. |
| angle bisector | a ray that divides an angle into two adjacent angles that are congruent.` |
| vertical angles | two angles whose sides form two pairs of opposite rays. |
| linear pair | two adjacent angles whose non-common sides form one pair of opposite rays. |
| conditional statement | has two parts: a hypothesis and a conclusion. |
| if/then form | conditional statement where "if" is the hypothesis & then is the conclusion. |
| parallel lines | lines that are coplanar and do not intersect. |
| skew lines | not coplanar and do not intersect. |
| parallel planes | planes that dont intersect. |
| law of detachment | if p to q is a true statement, & p is true, then q is true. |
| law of syllogism | if p to q is a true statement & q to r is a true statement then p to r is true. |
| converse | switches the hypothesis and the conclusion. |
| inverse | makes the hypothesis and conclusion negative. |
| contrapositive | negation of the converse. |
| construction | a geometric drawing using a limited set of tools, using a straight edge. |
| conjecture | an un-proven statement that is based on observations. |
| counterexample | example that shows a conjecture is false. |
| point | no dimension, represented by a small dot. |
| line | extends in one dimension. usually represented by a straight line w/two arrowheads to indicate that the line extends without end in two directions. |
| plane | extends in 2 dimensions. usually represented by a shape that looks like a table top or wall. |
| intersection | set of points a figure has in common. |
| postulate | rules accepted without proof. |
| coordinate | real #s that corresponds to a point. |
| angle | consists of different rays that have the same initial point. |
| rays | sides of an angle. |
| vertex | initial point of angle. |
| interior | between points that lie on each side of the angle. |
| exterior | not on the angle or inits interior. |
| adjacent angles | share a common vertex & side, but have no common initial points. |
| perpendicular lines | intersect to form a right angle. |
| addition property | if a = b, then a + c = b + c. ex: x = y, then x + 2 = y + 2. |
| subtraction property | if a = b then a - c = b - c |
| multiplication property | If a=b, then ac = bc |
| division property | If a=b, then a/c=b/c |
| substituiton property | if A = B then a can be substituited for b in an equation or expression. |
| reflexive property | For any real number a, a=a |
| symmetric property | If a = b, then b = a |
| transitive property | If a = b and b = c, then a = c. |
| linear pair postulate | if 2 angles form a linear pair, then they are supplementary |
| parallel postulate | if there is a line and a point not on that line, then there is exactly one line through the point parallel to the given line. |
| perpendicular postulate | if there is a line, and a point not on that line, then there is exactly one line thru the point perpendicularto the given line. |
| corresponding angles postulate | if 2 parallel linees are cut by a transversal, corresponding angle pairs are congruent. |
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