18 terms

substitution, reflexive, symmetric, transitive properties of equality and congruence
midpoint, angle bisector, segment addition, angle addition postulates and definitions

Substitution Property of Equality

If x = 5 then x + y = 5 + y

Reflexive Property of Equality

m<A = m<A

Reflexive Property of Congruence

<A ≅ <A

Transitive Property of Equality

If a = b and b = x + 7 then a = x + 7

Transitive Property of Congruence

If <A ≅ <B and <B ≅ <M then <A ≅ <M

Definition of Midpoint

If D is the midpoint of segment AB then AD = DB and segment AD ≅ segment DB.

Definition of Angle Bisector

If ray XY bisects <PXR then m<PXY = m<YXR

and <PXY ≅ <YXR

and <PXY ≅ <YXR

Segment Addition Postulate

If D is between A and B then AD + DB = AB

Angle Addition Postulate

If ray XY is between the two sides of <PXR then

m<PXY + m<YXR = m<PXR

m<PXY + m<YXR = m<PXR

Complementary Angles Definition

Two angles whose measures add to 90 degrees.

Supplementary Angles Definition

Two angles whose measures add up to be 180 degrees.

Vertical Angles Definition

Two non-adjacent angles formed by intersecting lines.

Vertical Angles Theorem

Vertical angles are congruent.

Definition of Perpendicular Lines

If two lines are perpendicular they form a right angle. or

If two lines form a right angle they are perpendicular.

If two lines form a right angle they are perpendicular.

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

Perpendicular Line Theorem

If two lines form congruent adjacent angles then the lines are perpendicular.

Converse of Perpendicular Theorem

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

Complementary Angles Theorem

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

Converse of Complementary Angle Theorem