Postulates & Properties of Equality

Postulate

Statement accepted to be true without proof

Two Point Postulate

Through any 2 points, there exists exactly one line

Line Point Postulate

A line contains at least 2 points

Line Intersection Postulate

If 2 lines intersect, then their intersection is exactly one point

Three Point Postulate

Through any 3 noncollinear points, there exists exactly one plane

Plane-Point Postulate

A plane contains at least 3 noncollinear points

Plane-line Postulate

If 2 points lie in a plane then the line containing them lies in the plane

Plane Intersection Postulate

If two planes intersect, then their intersection is a line

A line is perpendicular to a plane if…

the line intersects the plane at a point and perpendicular to every line in the plane that intersects it at a point

Addition Property

1. If a=b, then a+c=b+c

2. If AB=CD, then AB+EF=CD+EF

Subtraction Property

If a=b, then a-c=b-c

Multiplication Property

If a=b, then a+c=b+c

Division Property

1. If a=b and c is not equal to 0, then a/c=b/c

2. If 2AB=2CD, then AB=CD

Substitution Property

If a = b, then a can be substituted for b in an equation or expression

Reflexive Property

a=a, AB=AB

Symmetric Property

If a=b, then b=a; if AB=CD, then CD=AB

Transitive Property

If a=b and b=c, then a=c

If x+7=-10, then x=-17

Subtraction PofE

If m<A=m<B, then m<A + m<C = m<B + m<C

Addition PofE

If x-9=2 and x=11, then 11-9=2

Substitution PofE

Multiplication PofE

If a=8, then 8=a

Symmetric PofE

If AB + BC = AC and AC=10, then AB + BC = 10

Transitive PofE

m<A = m<A

Reflexive PofE

If 3(x-4)=15, then 3x-12=15

Distributive PofE

If 4x=32, then x=8

Division PofE

If AB + BC = AC and AB = 50, then 50 + BC = AC

Substitution PofE

True or False: Planes W and X intersect at line KL

True

True or False: Points K, L, M, and N are coplanar

False

True or False: Points Q, J, and M are collinear

False

True or False: Line MN and line RP intersect

False

True or False: Line JK lies in plane X

True

True or False: <PLK is a right angle

False

True or False: <NKL and <JKM are vertical angles

True

<NKJ and <JKM are supplementary angles

True

What Postulate is this an example of? Line Q contains points J and K

Line-Point Postulate

What Postulate is this an example of? Lines P and Q intersect at point H

Line Intersection Postulate

What Postulate is this an example of? Through points J, G, and L exists on plane m

Three Point Postulate

What Postulate is this an example of? Points H and G lie in plane m, therefore line p must also lie in plane m

Plane-Line Postulate