Math Terms

Segment Addition Postulate

B is between A and C , then AB +BC= AC

Midpoint

A point that divides a segment into two congruent segments

Segment bisector

a ray segment or line that intersects a segment at its midpoint

Congruent

the same size and shape, having equal measure

Point

location in space represented by a dot

Line

A straight path that extends forever in two directions

Plane

A flat surface that extends forever in two directions

Line segment

a portion of a line with two endpoints, also called a segment

Ray

A portion of a line with one endpoint that extends forever in one direction

Opposite rays

2 rays going in opposite directions that share a common endpoint

collinear

points on the same line

coplanar

points on the same plane and lines

Angle

formed by two rays with a common endpoint

Sides

rays

Vertex

endpoint

Notation

how many names an angle could have

Congruent Angles

Angles with the same measure

Adjacent Angles

2 coplanar angles with a common side, common vertex, but no common interior points ( no overlap)

Bisector of an angle

Ray that cuts an angle into two congruent angles

Angle Addition Postulate

If a point B lies in the interior of angle AOC, then measure angle AOB+ Measure angle BOC= Measure angle AOC

Parallel Lines

Coplanar lines that have the same slope and don’t intersect

Skew lines

Noncoplanar lines that do not intersect

Perpendicular Lines

Lines that intersect to make 90 degrees

Complementary Angles

2 Angles that add up together and form a right angle

Supplementary Angles

2 Angles that can add up to make a 180 degree line

Vertical Angles

Non adjacent angles formed by two intersecting lines

Addition Property (Add. Prop)

If a=b and c=d then a+c= b+d

Subtraction Property ( Subt. Prop.)

If a= b and c=d then a-c=b-d

Multiplication Property (Mult. Prop.)

If a=b then ca=cb

Division Property (Div. Prop.)

If a=b and c=0 then a/c=b/c

Substitution Property (Subs. Prop.)

If a=b, then either a or b may be substituted for the other in any equation

Reflexive Property (Ref. Prop.)

a=a

Symmetric Property (Symm. Prop.)

If a=b then b=a

Transitive Property (Trans. Prop.)

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

Postulate( Post.)

• Accept as true

• Never prove true

• Use in proofs

• Use to help prove theorems true

Theorems(Thm.)

• Must prove true before using them

• Once proven true, you can use them

Midpoint Theorem (Mdpt. Thm.)

If M is the midpoint of seg. AB, then AM= ½ AB and MB= ½ AB

Angle Bisector Theorem (< Bis. Thm)

If ray BX is the Bisector of < ABC, then m<ABX=1/2 m<ABC and M< XBC=1/2 m<ABC.

Vertical Angle Theorem (VA Thm)

If 2 Angles are vertical, then they are congruent

Adj. Acute. Angle Theorem

If the exterior sides of two adjacent acute angles are perpendicular, then the angles are complementary.

Perpendicular Theorem

If two lines are perpendicular, then they form congruent adjacent angles

Supplements of Congruent Angles Theorem

If two angles are supplements of congruent angles then the 2 Angles are congruent

Complements of Congruent Angles Theorem

If two angles are complements of congruent angles then the 2 angles are congruent

Parallel Planes

Planes that do not intersecet

Transversal

Is a line that intersects two or more coplanar lines in different points

Corresponding Angles

Same Side Interior Angles (SSI/ SSIA)

Alternate Interior Angles (AIA)

Alternate Exterior Angles (AEA)

Parallel Planes Theorem ( // Planes Thm.)

If two parallel planes are cut by a third plane, then the lines of intersection are parallel

Perpendicular Transversal Theorem ( T. Transv. Thm.)

If Transversal is perpendicular to one of the two parallel lines, then it is perpendicular to the other line

CA Postulate (CA. Post.)

If two parallel lines are cut by a transversal then CA are congruent.

AIA Theorem (AIA Thm.)

If two parallel lines are cut by a transversal then AIA are congruent

AEA Theorem (AEA Thm.)

If two parallel lines are cut by transversal then AEA are congruent

SSI Theorem (SSI/SSIA Thm.)

If two parallel lines are cut by a transversal then SSI/SSIA are supplementary