Geometry Trig 2Name______________ Unit 2.2Date _______________ Properties of Algebra Properties of Equality DefinitionExample Addition PropertyIf a = b and c= d then a+c=b+d if x = 4 then X+2=4+2 Subtraction PropertyIf a = b and c= d then a- c=b-d if x = 4 then X-2=4-2 Multiplication PropertyIf a=b then ac=bc if x = 4 then 2X=2(4) Division PropertyIf a=b and c≠0, then a/c = b/c if x = 4 then X/2=4/2 Substitution PropertyIf a=b then either a or b may be substituted for the other in any equation. If x = 4 and x+y = 6 Then 4+y = 6 **REPLACING WITH ITS EQUAL** Distributive Propertya(b+c)= ab+ac If 6(x+1) then 6x+6 Reflexive Propertya=a AB=AB Symmetric PropertyIf a=b then b=a If x = 4 then 4 = x Transitive PropertyIf a=b and b=c then a=c If x= y and y = 4 then x=4 Properties of Congruence DefinitionExample Reflexive Property aaaa Symmetric Property If a  b then b  a Transitive Property If a  b and b  c then a  c

Statements and Reasons for Proofs Properties, Definitions, Postulates, Theorems SketchIFTHEN Segment Addition Postulate If B is between A and C Then AB+BC = AC Angle Addition Postulate If B is in the interior of  AOC Then  AOB +  BOC=  AOC Angle Addition Postulate (straight angle) If  XYZ is a straight angle and A is in the interior Then  XYA +  AYZ= 180 Definition of Angle Bisector If TP bisects  STAThen  1=  2 Definition of Midpoint If B is the midpoint of AC Then AB = BC Definition of Complementary Angles If 2 angles are complementary Then they total 90 or  MNP+  PNO=90 Definition of Supplementary Angles If 2 angles are supplementary Then they total 180 or  1+  2=180 Vertical Angle Theorem If  1 and  2 are vertical angles Then  1=  2 A BC A B C A O C B S T R P 2 1 M N O P A Z Y X 1 2

Statements and Reasons for Proofs Properties, Definitions, Postulates, Theorems SketchIFTHEN Midpoint Theorem If B is the midpoint of AC Then AB = ½ AC and BC = ½ AC Angle Bisector Theorem If YR bisects  XYZ Then  XYR= ½  XYZ and  RYZ= ½  XYZ Definition of Perpendicular Lines If 2 lines are  If a  b Then they form right angles Then  1=  2 Definition of Right Angles If an angle is a right angle Then it measures 90  If 2 lines are  If a  b Then they form  adjacent angles Then  1  2  If 2 lines form  adjacent angles If  1  4 Then the lines are  Then a  b  complementary If the exterior sides of 2 adjacent acute angles are  If a  b Then the angles are complementary Then  1+  2=90 Supplementary Angle Theorem If 2 angles are supplements of  angles Then the angles are  A B C X Y Z R a b 2 1 a b 2 1 a b 2 1 a b 4 1 a b

Statements and Reasons for Proofs Properties, Definitions, Postulates, Theorems SketchIFTHEN