# Shared Flashcard Set

## Details

Geometry Postulates, Definitions and Theorems
Geometry Postulates, Definitions and Theorems
77
Mathematics
11/04/2013

Term
 Colinear Points
Definition
 Points on the same line
Term
 Coplanar Points
Definition
 Points that lie on the same plane
Term
 Ray
Definition
 Consists of an endpoint and all the points in one direction
Term
 Line Segment
Definition
 Consists of two endpoints and all the points between them
Term
 Opposite Ray
Definition
 If Point C lies on AB between point A and point B, then CA and CB are opposite rays.
Term
 Intersection
Definition
 The set of all points the figures have in common
Term
 Midpoint
Definition
 Take average of numbers
Term
 Distance
Definition
 Pythagorean's Theorem
Term
 Angle Bisector
Definition
 A ray that divides an angle into two congruent angles
Term
 Conjecture
Definition
 Unproven statement based off of observations
Term
 Inductive Reasoning
Definition
 If pattern, then make conjecture
Term
 Conditional Statement
Definition
 A logic statement with two parts (Hypothesis→Conclusion)
Term
 Biconditional Statement
Definition
 Contains phrase "If and only if" (iff) Any true definition can be written as this statement
Term
 Law Of Detachment
Definition
 If true hypothesis of true Conditional, then true conclusion.
Term
 Law of Syllogism
Definition
 If hypothesis (p), then conclusion (q). If hypothesis (q), then conclusion (r). If hypothesis (p), then conclusion (r).
Term
 Postulate 5
Definition
 If two points, then one line
Term
 Postulate 6
Definition
 If one line, then at LEAST 2 points
Term
 Postulate 7
Definition
 If 2 intersecting lines, then one intersection point
Term
 Postulate 8
Definition
 If 3 noncollinear points, then one plane
Term
 Postulate 9
Definition
 If one plane, then at LEAST 3 noncollinear points
Term
 Postulate 10
Definition
 If two points in one plane, then line is in plane
Term
 Postulate 11
Definition
 If two planes intersect, then intersection is one line
Term
Definition
 If a=b, then a+c=b+c
Term
 Subtraction Property of Equality
Definition
 If a=b, then a-c=b-c
Term
 Multiplication Property of Equality
Definition
 If a=b, then a•c=b•c
Term
 Division Property of Equality
Definition
 If a=b and C≠0, then a/c=b/c
Term
 Substitution Property of Equality
Definition
 If a=b, then a can be substituted for b in any equation
Term
 Distributive Property
Definition
 a(b+c)= ab+ac
Term
 Reflexive Property of Equality
Definition
 a=a
Term
 Symmetric Property of Equality
Definition
 If a=b, then b=a
Term
 Transitive Property of Equality
Definition
 If a=b and b=c, then a=c
Term
 Theorem 2.3: Right Angles Theorem
Definition
 If 2 angles are right, then congruent
Term
 Theorem 2.4: Congruent Supplements Theorem
Definition
 If2 angles are supplementary to same angle, then congruent
Term
 Theorem 2.5: Congruent Complements Theorem
Definition
 If 2 angles are complementary to the same angle, then congruent
Term
 Postulate 12: Linear Pair Postulate
Definition
 If 2 angles form linear pair, then supplementary
Term
 Theorem 2.6: Vertical Angles Congruence Theorem
Definition
 Vertical angles are congruent
Term
 Skew Lines
Definition
 If two lines are not coplanar and do not intersect, they are skew
Term
 Postulate 13: Parallel Postulate
Definition
 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
Term
 Postulate 14: Perpendicular Postulate
Definition
 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
Term
 Alternate Interior Angles
Definition
 Opposite sides of transversal on inside of parallel line [image]
Term
 Alternate Exterior Angles
Definition
 Angles on opposite sides of transversal and on the outside of the parallel lines [image]
Term
 Corresponding Angles
Definition
 An angle that is in the same spot of another group of angles [image]
Term
 Consecutive interior angles
Definition
 Between two lines on same side of transversal [image]
Term
 Postulate 15: Corresponding Angles Postulate
Definition
 If two parallel lines are cut by a transversal, then corresponding are congruent
Term
 Thm 3.1: Alternate Interior Angles Theorem
Definition
 If two parallel lines are cut by a transversal, then alternate interior are congruent
Term
 Thm 3.2: Alternate Exterior Angles Theorem
Definition
 If two parallel lines are cut by a transversal, then alternate exterior are congruent
Term
 Thm 3.3: Consecutive Interior Angles Theorem
Definition
 If two parallel lines are cut by a transversal, then consecutive interior angles are SUPPLEMENTARY
Term
 Postulate 16: Corresponding Angles Converse Postulate
Definition
 If two lines cut by transversal and corresponding angles are congruent, then lines are parallel
Term
 Thm 3.4: Alternate Interior Angles Converse Theorem
Definition
 If two lines are cut by a transversal and alternate interior are congruent, then lines are parallel
Term
 Thm 3.5: Alternate Exterior Angles Converse Theorem
Definition
 If two lines are cut by transversal and alternate exterior angles are congruent, then lines are parallel
Term
 Thm 3.6: Consecutive Interior Angles Converse Theorem
Definition
 If two lines are cut by a transversal and Consecutive interior angles are SUPPLEMENTARY, then lines are parallel
Term
 Postulate 17: Slopes of Parallel lines
Definition
 Two nonvertical lines are parallel IFF (if and only if) they have the same slope
Term
 Slopes of Perpendicular Lines
Definition
 Two nonvertical lines are perpendicular IFF the product of their slopes is -1. *Horizontal and vertical lines ARE parallel
Term
 Thm 3.7: Transitive Property of Parallel Lines
Definition
 If two lines are parallel to same line, then parallel to eachother
Term
 Thm 3.8: Congruent Linear Pair→ Perpendicular
Definition
 If two lines intersect and form linear pair of congruent angles, then lines are perpendicular
Term
 Thm 3.9: Perpendicular Form 4 Right Angles
Definition
 If two lines are perpendicular, then the 4 angles are right
Term
Definition
 If sides of two acute angles are perpendicular, then angles are complementary
Term
 Thm 3.11: Perpendicular Transversal Theorem
Definition
 If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other
Term
 Thm 3.12: Lines Perpendicular to a Transversal Theorem
Definition
 (CANNOT BE SKEW!)→In a plane, if two lines are perpendicular to the same line, then they are parallel
Term
 Thm 4.1: Triangle Sum Theorem
Definition
 [image]
Term
 Thm *: Linear Pair =180 Theorem
Definition
 [image]
Term
 Thm 4.2: Exterior Angle Theorem
Definition
 [image]
Term
 Corollary to Triangle Sum Theorem
Definition
 [image]
Term
 Thm 4.3: Third Angles Theorem
Definition
 [image]
Term
 Thm 4.4: Property fo Congruent Triangles
Definition
 Reflexive: ABC ≡ ABC Symmetric: If ABC ≡ DEF, then DEF ≡ ABC Transitive: ABC ≡ DEF, DEF ≡ GHJ, then ABC ≡ GHJ
Term
 Postulate 19: Side-Side-Side (SSS post) congruence Postulate
Definition
 [image]
Term
 Postulate 19: side-side side congruence postulate (sss post)
Definition
 [image]
Term
 Postulate 20: angle-side-angle Postulate (ASA post)
Definition
 [image]
Term
 Postulate 21: Side-Angle-Side Postulate (SAS Post)
Definition
 [image]
Term
 Theorem 4.6: Angle-Angle-Side Congruence Theorem (AAS Thm)
Definition
 [image]
Term
 Theorem 4.5: Hypotnuse-Leg Congruence Theorem
Definition
 [image]
Term
 Thm 4.7: Base Angles Theorem
Definition
 If two sides of a triangle are congruent, then the angles opposite them are congruent
Term
 Thm 4.8: Base Angles Converse Theorem
Definition
 [image]
Term
 Corollary to Base Angles Theorem
Definition
 If equalateral, then equangular
Term
 Corollary to Base Angles Converse Theorem
Definition
 If equangular then equalteral
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