Geomentry Reference
Linear Pair Definition
<1 is supp to <2
Definition of Angle Bisector
A line that splits an angle into two equal angles.
Definition of right angle
A right angle = 90 degrees Angle ABC is 90*
Definition of supplementary angles
A supp angle = 180 <ABC = 180
Congruent Angles (Definition)
Angles which have the same measure
Definition of a line
Extends in both directions without end and has no thickness
Linear Pair Theorem
If 2 angles form a linear pair, then they are supplementary
Right Angle theorem
If <G, <H are right angles then,<G is congruent to <H it specifies more on which angles add up to 90
Congruence Complements Theorem
If <M is supp to <N and <Q is supp to <N then <M congruent <Q
Segment Addition Postulate
If B is between A and C, then AB + BC = AC
Symmetric Property of Equality
If a = b, then b = a
Substitution Property of Equality
If a=b, then b can be substituted for a in any expression
Congruent Supplements Theorem
If two angles are supplementary to the same angle, then they are congruent
Vertical Angles Congruence Theorem
If two angles are vertical angles, then they are congruent.
Vertical Angles Theorem
If two angles are vertical angles, then they are congruent.
perpendicular
Intersecting at or forming right angles
definition of congruence segments
Segments are congruent if and only if they have the same measure
Definition of a plane
Three noncollinear points determine a plane.
Definition of complementary angles
Two angles whose sum is 90 degrees
Addition POC/POE
XY = WZ, then XY+TU = WZ+TU adding TU to both sides
Substitution POE
a + b = 2, b=1 ---> a + 1 = 2 Replacing something
reflexive property of equality
a = a (any number is equal to itself)
Point (definition) math
a point indicates the place something is
Midpoint Definition
a point that divides a segment into 2 congruent segments
Distributive Property of Equality
a(b + c) = ab + ac
Distributive POE
a(b+c) = ab + bc
Transitive Property of Equality
a=b and b=c then a=c (similar to law of syllogism)
Def of congruent angles
angles that have = measurements
Multiplication Property of Equality
if 1/2x = 5 then x = 10
Division Property of Equality
if a = b and c is not equal to 0, then a/c = b/c Ex: 3AB = CD then AB = 1/3CD
defintion of congruence
if line MN confruent to line OP then MO congruent to NP
Congruent Complements Theorem
if two angles are complementary to the same angle, then they are congruent Ex: <1 comp to <2 <2 is comp to <3 <1 is congruent to <3
Supplementary Angles Theorem
m<1 + m<2 = 180
Definition of Congruent Segments
segments that have the same length
congruent segments defn
segments that have the same length
Definition of Vertical Angles
two angles whose sides form two pairs of opposite rays
Definition of intersection
when a line passes through something
what is subtraction POE/POC?
x + 3 = y ---> x = y - 3 subtracted the 3 on both sides