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

Additional Mathematics Flashcards

 


 

Cards

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
Addition Property of Equality
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
Thm 3.10: Two Adjacent Perpendicular→Congruent
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