Algebra Class 2-6 to 2-8 Proofs Flashcards

Algebraic Proofs

• The Addition Property states: If a = b, then a + c = b + c.
• The Subtraction Property states: If a = b, then a - c = b - c.
• The Multiplication Property states: If a = b, then a × c = b × c.
• The Division Property states: If a = b and c ≠ 0, then a/c = b/c.

Properties of Equality

• The Reflexive Property indicates that a = a for any value a.
• The Symmetric Property asserts: If a = b, then b = a.
• The Transitive Property specifies: If a = b and b = c, then a = c.
• The Substitution Property allows for the replacement of a with b in any equation or expression if a = b.

Distributive Property

• The Distributive Property expresses that a(b + c) = ab + ac.

Segment Proofs

• The Segment Addition Postulate explains that if points A, B, and C are collinear, point B is between A and C if and only if AB + BC = AC.

Properties of Congruence

• The Reflexive Property of Congruence states: Segment AB is congruent to itself (AB ≅ AB).
• The Symmetric Property of Congruence maintains that if segment AB ≅ segment CD, then segment CD ≅ segment AB.
• The Transitive Property of Congruence specifies: If segment AB ≅ segment CD and segment CD ≅ segment EF, then segment AB ≅ segment EF.

Geometric Concepts

• Point D is defined as being in the interior of a segment or angle.