proofs

Definition of Congruence

switch from squiggly line on equal sign to not and other way around

Definition of Midpoint

Part = Part (middle dot cuts a line in half).

Definition of Angle Bisector

a line that splits a corner into two equal smaller corners.

Definition of Segment Bisector

Part = Part

Definition of Complementary Angles

Corner + Corner = 90°

Definition of Supplementary Angles

Corner + Corner = 180°

Definition of Perpendicular Lines

if one of the angles equals 90

Definition of Right Angles

angle + angle = 90

Linear Pair Postulate

Line = 180° (angles next to each other on a line add to 180°). 

Vertical Angles Theorem

when it’s an X and one is 60 so the other one is 60

Angle Addition Postulate

angle + angle =whole

Segment Addition Postulate

segment +segment = whole

• Congruent Complement Theorem

If A + C = 90 and B + C = 90 then A = B

• Congruent Supplement Theorem

If A + C = 180 and B + C = 180 then A = B

• Reflexive

• Something equals itself (A = A)

• Symmetric

• Flip both sides (If A = B, then B = A).

• Addition / Subtraction

• Add or subtract same thing on both sides.

• Multiplication / Division

• Multiply or divide same thing on both sides.

• Substitution

• Swap equal parts.

• Transitive

You use Substitution when two angles are equal, and you swap one name for the other:

Given: m\angle A = B

Equation: m\angle A + C = 180

New Equation: m\angle B + C = 180

Reason: Substitution Property (swapped A out for B)