Geometric Proof Properties

Addition Property of Equality

If a = b, then a + c = b + c

Subtraction Property of Equality

If a = b, then a - c = b - c

Multiplication Property of Equality

If a = b, then ac = bc

Division Property of Equality

If a = b, then a/c = b/c, c can not = 0

Substitution Property of Equality

If AB = CD and AB + DE = 10, then CD + DE = 10

Distributive Property

a(b + c) = ab + ac

Reflexive Property of Equality

m∠A = m∠A

Symmetric Property of Equality

If a = b, then b = a

Transitive Property of Equality

If MN = NO and NO = OP, then MN = OP

Combine Like Terms

If 6y + 15 - 9 + 10y, then 16y + 6

Angle Addition Postulate

If P is in the interior of ∠RST, then

m∠RST = m∠RSP + m∠PST

Segment Addition Postulate

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

Linear Pair Postulate/Supplement Theorem

∠1 and ∠2 form a linear pair, then ∠1 and ∠2 are supplementary

Definition of Complimentary Angles

If ∠RST and ∠RSP form a right angle in a figure, then m∠RST + m∠RSP = 90°

Definition of Supplementary Angles

If ∠GHI and ∠IHJ form a straight line in a figure, then m∠GHI + m∠IHJ = 180°

Definition of Perpendicular Lines

If KL ⊥ LM, then ∠KLM is a right angle

Definition of Congruent Angles

If m∠DEF = m∠UVW, then ∠DEF ≅ ∠UVW

Definition of Congruent Segments

If KP ≅ LP, then KP = LP

Definition of Angle Bisector

If ray XY bisects ∠AXB, then ∠AXY ≅ ∠YXB

Definition of Midpoint

If point O is the midpoint of GH, then GO≅OH

Vertical Angles Theorem

Given the figure, then ∠2 ≅ ∠4

Definition of Segment Bisector

If ray JK bisects YZ at point J, then YJ≅JZ

All right angles are congruent

If ∠ABC and ∠XYZ are right angles, then ∠ABC ≅ ∠XYZ

Reflexive Property of Congruence

∠A≅∠A

Symmetric Property of Congruence

If ∠A≅∠B, then ∠B≅∠A

Transitive Property of Congruence

If ∠A≅∠B and ∠B≅∠C , then ∠A≅∠C

Given

The first statement in every proof.