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| Points that lie on the same plane |
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| Consists of an endpoint and all the points in one direction |
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| Consists of two endpoints and all the points between them |
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If Point C lies on AB between point A and point B, then CA and CB are opposite rays.
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| The set of all points the figures have in common |
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| A ray that divides an angle into two congruent angles |
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| Unproven statement based off of observations |
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| If pattern, then make conjecture |
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A logic statement with two parts
(Hypothesis→Conclusion) |
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| Contains phrase "If and only if" (iff) Any true definition can be written as this statement |
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| If true hypothesis of true Conditional, then true conclusion. |
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| If hypothesis (p), then conclusion (q). If hypothesis (q), then conclusion (r). If hypothesis (p), then conclusion (r). |
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| If two points, then one line |
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| If one line, then at LEAST 2 points |
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| If 2 intersecting lines, then one intersection point |
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| If 3 noncollinear points, then one plane |
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| If one plane, then at LEAST 3 noncollinear points |
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| If two points in one plane, then line is in plane |
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| If two planes intersect, then intersection is one line |
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| Addition Property of Equality |
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| Subtraction Property of Equality |
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| Multiplication Property of Equality |
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| Division Property of Equality |
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Definition
| If a=b and C≠0, then a/c=b/c |
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| Substitution Property of Equality |
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| If a=b, then a can be substituted for b in any equation |
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| Reflexive Property of Equality |
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| Symmetric Property of Equality |
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| Transitive Property of Equality |
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| Theorem 2.3: Right Angles Theorem |
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| If 2 angles are right, then congruent |
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| Theorem 2.4: Congruent Supplements Theorem |
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| If2 angles are supplementary to same angle, then congruent |
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| Theorem 2.5: Congruent Complements Theorem |
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| If 2 angles are complementary to the same angle, then congruent |
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| Postulate 12: Linear Pair Postulate |
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| If 2 angles form linear pair, then supplementary |
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| Theorem 2.6: Vertical Angles Congruence Theorem |
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| Vertical angles are congruent |
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| If two lines are not coplanar and do not intersect, they are skew |
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| Postulate 13: Parallel Postulate |
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| If there is a line and one point and that point is not on the line, then on that point there is one line that is parallel to the other line |
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| Postulate 14: Perpendicular Postulate |
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| If there is a line and one point and that point is not on the line, then on that point there is one line that is perpendicular to the other line |
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| Alternate Interior Angles |
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Opposite sides of transversal on inside of parallel line
[image] |
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| Alternate Exterior Angles |
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Angles on opposite sides of transversal and on the outside of the parallel lines
[image] |
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An angle that is in the same spot of another group of angles
[image] |
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| Consecutive interior angles |
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Between two lines on same side of transversal
[image] |
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| Postulate 15: Corresponding Angles Postulate |
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| If two parallel lines are cut by a transversal, then corresponding are congruent |
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| Thm 3.1: Alternate Interior Angles Theorem |
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| If two parallel lines are cut by a transversal, then alternate interior are congruent |
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| Thm 3.2: Alternate Exterior Angles Theorem |
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| If two parallel lines are cut by a transversal, then alternate exterior are congruent |
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| Thm 3.3: Consecutive Interior Angles Theorem |
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| If two parallel lines are cut by a transversal, then consecutive interior angles are SUPPLEMENTARY |
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| Postulate 16: Corresponding Angles Converse Postulate |
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Definition
| If two lines cut by transversal and corresponding angles are congruent, then lines are parallel |
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| Thm 3.4: Alternate Interior Angles Converse Theorem |
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| If two lines are cut by a transversal and alternate interior are congruent, then lines are parallel |
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| Thm 3.5: Alternate Exterior Angles Converse Theorem |
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| If two lines are cut by transversal and alternate exterior angles are congruent, then lines are parallel |
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| Thm 3.6: Consecutive Interior Angles Converse Theorem |
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| If two lines are cut by a transversal and Consecutive interior angles are SUPPLEMENTARY, then lines are parallel |
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| Postulate 17: Slopes of Parallel lines |
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| Two nonvertical lines are parallel IFF (if and only if) they have the same slope |
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| Slopes of Perpendicular Lines |
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Two nonvertical lines are perpendicular IFF the product of their slopes is -1.
*Horizontal and vertical lines ARE parallel |
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| Thm 3.7: Transitive Property of Parallel Lines |
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| If two lines are parallel to same line, then parallel to eachother |
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Thm 3.8: Congruent
Linear Pair→ Perpendicular |
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| If two lines intersect and form linear pair of congruent angles, then lines are perpendicular |
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| Thm 3.9: Perpendicular Form 4 Right Angles |
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| If two lines are perpendicular, then the 4 angles are right |
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| Thm 3.10: Two Adjacent Perpendicular→Congruent |
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| If sides of two acute angles are perpendicular, then angles are complementary |
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| Thm 3.11: Perpendicular Transversal Theorem |
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| If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other |
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| Thm 3.12: Lines Perpendicular to a Transversal Theorem |
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| (CANNOT BE SKEW!)→In a plane, if two lines are perpendicular to the same line, then they are parallel |
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| Thm 4.1: Triangle Sum Theorem |
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| Thm *: Linear Pair =180 Theorem |
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| Thm 4.2: Exterior Angle Theorem |
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Definition
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| Corollary to Triangle Sum Theorem |
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| Thm 4.3: Third Angles Theorem |
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| Thm 4.4: Property fo Congruent Triangles |
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Definition
Reflexive: ABC ≡ ABC
Symmetric: If ABC ≡ DEF, then DEF ≡ ABC
Transitive: ABC ≡ DEF, DEF ≡ GHJ, then ABC ≡ GHJ
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| Postulate 19: Side-Side-Side (SSS post) congruence Postulate |
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| Postulate 19: side-side side congruence postulate (sss post) |
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| Postulate 20: angle-side-angle Postulate (ASA post) |
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| Postulate 21: Side-Angle-Side Postulate (SAS Post) |
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| Theorem 4.6: Angle-Angle-Side Congruence Theorem (AAS Thm) |
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| Theorem 4.5: Hypotnuse-Leg Congruence Theorem |
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| Thm 4.7: Base Angles Theorem |
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| If two sides of a triangle are congruent, then the angles opposite them are congruent |
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| Thm 4.8: Base Angles Converse Theorem |
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| Corollary to Base Angles Theorem |
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Definition
| If equalateral, then equangular |
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| Corollary to Base Angles Converse Theorem |
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| If equangular then equalteral |
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