Download Postulates, Theorems and Properties for Geometric Proofs

1)
SAP (Segment Addition Postulate)
AB + BC = AC
2) AAP (Angle Addition Postulate)
mABD  mDBC  mABC
3) Reflexive Property (For Both Equality and Congruency)
AB = AB or AB  AB
mA  mA or A  A
4) Symmetric Property (For Both Equality and Congruency)
If AB  CD then CD  AB or AB = CD then CD = AB
If mA  mB then mB  mA or If A  B then B  A
5) Transitive Property (For Both Equality and Congruency)
If AB = CD and CD = EF then AB = EF
If AB  CD and CD  EF then AB  EF
If A  B and B  C then A  C
If mA  mB and mB  mC then mA  mC
6) Addition Property (For Both Equality and Inequality)
If a = b then a + c = b + c
If a < b then a + c < b + c
7) Subtraction Property (For Both Equality and Inequality)
If a = b then a - c = b - c
If a < b then a - c < b – c
8) Multiplication Property (For Both Equality and Inequality)
If a = b then a x c = b x c
If a < b then a x c < b x c (if c is positive)
If a < b then a x c > b x c (if c is negative)
9) Division Property (For Both Equality and Inequality)
If a = b then a ÷ c = b ÷ c
If a < b then a ÷ c < b ÷ c (if c is positive)
If a < b then a ÷ c > b ÷ c (if c is negative)
10) Distributive Property
a(b + c) = ab + ac
ab + ac = a(b+c)
11) Definition of Congruent Angles
If mA  mB then A  B
If A  B then mA  mB
12) Definition of Congruent Segments
If AB  CD then AB = CD
If AB = CD then AB  CD
13) Definition of a Midpoint
If M is the midpoint of AB then AM  MB
If AM  MB then M is the midpoint of AB
14) Definition of an Angle Bisector
If BD is an angle bisector of ABC then ABD  DBC
If ABD  DBC then BD is an angle bisector of ABC
15) Substitution
If a = b the anywhere there is an (a), you may substitute a (b) and vice versa.
If mA  mB , then anywhere there is a mA , you may substitute a mB and vice versa.
16) Given
ENOUGH SAID…It’s the given!
17) All Right Angles Are Congruent
If  A and  B are right angles, then A  B
18) Two Angles Supplementary to the Same Angle Are Congruent
 A is supplementary to C
If
and  B is supplementary to C
then A  B
19) Two Angles Complementary to the Same Angle Are Congruent
If  A is complementary to C
and  B is supplementary to C
then A  B
20) All Linear Pairs are Supplementary
If 1 and 2 are a linear pair, then 1 and 2 are supplementary
21) Definition of Supplementary Angles
If 1 and 2 are supplementary, then m1  2  180
22) Definition of Complementary Angles
If 1 and 2 are complementary, then m1  2  90
23) All Vertical Angles are Congruent
1  3 and 2  4
24) Definition of Perpendicular Lines
If a  b then 1 and/or 2 and/or 3 and/or 4 is/are right angles.
If 1 and/or 2 and/or 3 and/or 4 is/are right angles then a  b .
25) Definition of a Right Angle
If 1 is a right angle, then m 1 =90
If m 1 =90, then 1 is a right angle