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| An unproven statement based on observations |
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| An example that shows the conjecture is false. |
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| 3 or more points that lie on the same line. |
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| 4 or more points that lie on the same plane. |
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| Two rays that connect at a middle point. |
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| A rule that is accepted without proof. |
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| Points on a line that can be matched up with real numbers. |
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| Segment Addition postulate |
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| If B is between A and C, then AB + BC = AC |
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| Segments that have the same length. |
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| Two rays with the same initial point. |
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| Angles that have the same measure. |
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| Each angle has a measure from 0 degrees to 180 degrees. |
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| Share a common vertex and a common interiorside. |
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| The point that divides the segment into two congruent parts. |
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| Any segment, ray, line of plane, that goes through the midpoint of a segment. |
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| A ray that divides an angle into two congruent adjacent angles. |
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| Angles whose sides form two pairs of opposite rays |
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| Two adjacent angles that form a straight line. |
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| Two angles whose sum is 90 degrees |
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| Two angles whose sum is 180 degrees. |
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| Two lines that intersect and form a right angle. |
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| Line perpendicular to a plane |
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Definition
| A line that intersects a plane in a point |
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Definition
| If p->q is true, and p is true, then q is true. |
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| Law of syllogism (Transitivity) |
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Definition
| If p->q and q->r, are both true,then p->r is true. |
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| Law of the contrapositive |
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Definition
| If a conditional p->q is true, then it's contrapositive, ~q->~p is also true. |
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| If you know the value of a variable, then you can plug it in. |
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| A statement that follows as a result of other true statements. All theorems must be proven in order to be considered a theorem. |
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| Right angle congruence theorem |
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Definition
| All right angles are congruent |
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| Congruent Supplements Theorem |
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Definition
| If two angles are supplementary to the same angle, then they are congruent to each other. |
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| Congruent complements theorem |
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Definition
| If 2 angles are complementary to the same angle, then they are congruent to each other. |
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| If 2 angles form a linear pair, then they are supplementary. |
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Definition
| If two angles are vertical angles, then they are congruent. |
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Definition
| Coplanar lines that never intersect |
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| Lines in different planes that never intersect |
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| Planes that don't intersect |
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| If there is a line and a point not on a line, then there is one line through the point parallel to the given line. |
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Definition
| If there is a line and a point not on the line, then thereis one line through the point perpendicular to the given line. |
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| If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular. |
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Definition
| If two sides of two adjacent acute angles are perpendicular, then the angles are complementary. |
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| If two lines are perpendicular, then they intersect to form four right angles. |
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| A line that intersects coplanar lines in two or more different points. |
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| Corresponding Angles postulate |
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Definition
| If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. |
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| Alternate interior angles theorem |
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Definition
| If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent |
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| Consecutive Interior angles theorem |
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Definition
| If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary. |
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| Alternate exterior angles theorem |
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Definition
| If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent. |
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| Perpendicular to parallels theorem |
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Definition
| If a transversal is perpendicular to one of two paralllel lines, then it is perpendicular to the other. |
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| Corresponding angles converse postulate |
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Definition
| If two lnes are cut by a transversal so that corresponding angles are congruent, then the lines are parallel. |
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| Alternate interior angles converse theorem |
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Definition
| If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel. |
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| Consecutive interior angles converse theorem |
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Definition
| If two lines are cut by a transversal so that consecutive ihnterior angles are supplementary , then the lnes are parallel. |
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| Alternate exterior angles converse theorem |
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Definition
| If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel. |
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| Transitivity of Parallels theorem |
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Definition
| If two lines are parallel to the same line, then they are parallel to each other. |
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| Two perpendiculars Theorem |
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Definition
| In a plane, if two lines are perpendicular to the same line, then they are parallel to each other. |
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