18 terms

Unit 1.1 Part 2 - Definitions, properties, postulates, theorems.

substitution, reflexive, symmetric, transitive properties of equality and congruence midpoint, angle bisector, segment addition, angle addition postulates and definitions
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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
If D is between A and B then AD + DB = AB
If ray XY is between the two sides of <PXR then
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 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