PROPERTIES, POSTULATES Flashcards
Can be true or false, most basic
Statement
The opposite of a statement
Negation
Has hypothesis first then conclusion
Conditional
If p then q,
Conditional statement
If q then p
Converse
If not p then not q
Inverse
If not q then not p
Contrapositive
If and only if
Bi conditional statement
Line segment postulate 5
Through any 2 points there exists exactly one line
Line postulate number 6
A line consists of at least 2 points
Line intersection postulate
If 2 lines intersect, their intersection is exactly 1 point
Plane postulate
Through any three non collinear points there exists exactly one plane
Plane postulate number 9
A plane consists of at least 3 non collinear points
Line in a plane postulate
If 2 points lie in a plane then the line containing the points is also in the plane
Plane intersection postulate
If 2 planes intersect then their intersection is a line
Angle addition postulate
If 2 angles have a common side and vertex, then the measure of the two angles is equal to the measure of the angle formed by the non shared sides
Segment addition postulate
If B is between A and C, then AB + BC=AC, if AB + BC=AC, then B is between A and C
Line segment postulate number 1
We can connect two points with a straight line and each point will correspond with a real number
If a=b, then a + c = b + c
Addition property of equality
If a=b, then a - c = b - c
Subtraction property of equality
A a=b, then ac=bc
Multiplication property of equality
If a=b, and c does not equal zero, then a/c=b/c
Division property of multiplication
If a=b
Substitution property of equality
If x=10 - 5, then x=5
Property of simplification
4(x-2)=4x-8
Distributive property
3=3, b=b,
Reflexive property
If a=b, then b=a
Symmetric property
If a=b and b=c, then a=c
Transitive
If a=b, then a + c = b + c
Addition property of equality
If a=b, then a - c = b - c
Subtraction property of equality
A a=b, then ac=bc
Multiplication property of equality
If a=b, and c does not equal zero, then a/c=b/c
Division property of multiplication
If a=b
Substitution property of equality
If x=10 - 5, then x=5
Property of simplification
4(x-2)=4x-8
Distributive property
3=3, b=b,
Reflexive property
If a=b, then b=a
Symmetric property
If a=b and b=c, then a=c
Transitive
Parallel lines and transversal postulate
If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent
Corresponding angles converse
if two lines are cut by a transversal so the corresponding angles are congruent, then the lines are parallel.
Alternate interior angles converse
if two lines are cut by a transversal so the alternate interior angles are congruent, then the lines are parallel.
Alternate exterior angles converse
if two lines are cut by a transversal so the alternate exterior angles are congruent, then the lines are parallel
Consecutive interior angles converse
if two lines are cut by a transversal so the consecutive interior angles are supplementary, then the lines are paralle
Perpendicular postulate 3.8
If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular
Perpendicular lines postulate 3.9
If two lines are perpendicular, then they intersect to form four right angles
Perpendicular lines postulate 3.10
If two sides of adjacent angles are perpendicular, then the angles are complementary
Perpendicular postulate 3.11
If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other
Perpendicular postulate 3.12
In a plane, if two lines are perpendicular to the same line, then they are parallel to each other
