Reasoning with Properties from Algebra

 Algebraic Properties of Equality:

• Additive Property: If c=d, then c + e = d + e

Where c, d and e are real numbers

• Subtractive Property: If c=d, then c-e = d-e

Where c, d and e are real numbers

• Multiplicative Property: If c=d, then ce = de

Where c, d and e are real numbers

• Divisive Property: If c=d, then c/e = d/e

Where c, d and e are real numbers

• Reflexive Property: c = c, for any real number c

• Symmetric Property: If c = d, then d = c

Where c, d are real numbers

• Transitive Property: If c = d and d = e, then c = e

Where c, d and e are real numbers

• Substitution Property: If c = d, then c can be substituted for d in any expression/equation. ( c and d are real numbers)

• Distributive Property: c ( d + e) = cd + ce

Where c, d and e are real numbers.

The above said properties are used all time while solving equations without even thinking about it.

When each step is written with a reason, then it is considered as a proof.

The above said can be used in geometry with segments and angles.

Properties of Equality in Segments:

• Reflexive Property: For any segment CD, CD = DC.
• Symmetric Property: If segment CD = segment EF, then segment EF = segment CD.
• Transitive Property: If segment CD = segment EF and segment EF = segment GH, then segment CD = segment GH

Properties of Equality in Angles:

• Reflexive Property: For any angle C, n<C = n<C
• Symmetric Property: For any C and B, if n<C = n<D, then, n<D = n<C
• Transitive Property: For any C, D and E, if n<C = n<D and n<D = n<E, then n<C = n<E.