Properties and Postulates
Proof Sheet Reflexive Property | A quantity is congruent (equal) to itself. a = a | Symmetric Property | If a = b, then b = a. | Transitive Property | If a = b and b = c, then a = c. | Addition Postulate | If equal quantities are added to equal quantities, the sums are equal. | Subtraction Postulate | If equal quantities are subtracted from equal quantities, the differences are equal. | Multiplication Postulate | If equal quantities are multiplied by equal quantities, the products are equal. (also Doubles of equal quantities are equal.) | Division Postulate | If equal quantities are divided by equal nonzero quantities, the quotients are equal. (also Halves of equal quantities are equal.) | Substitution Postulate | A quantity may be substituted for its equal in any expression. | Partition Postulate | The whole is equal to the sum of its parts.
Also: Betweeness of Points: AB + BC = AC
Angle Addition Postulate: m<ABC + m<CBD = m<ABD | Construction | Two points determine a straight line. | Construction | From a given point on (or not on) a line, one and only one perpendicular can be drawn to the line. | Right Angles | All right angles are congruent. | Straight Angles | All straight angles are congruent. | Congruent Supplements | Supplements of the same angle, or congruent angles, are congruent. | Congruent Complements | Complements of the same angle, or congruent angles, are congruent. | Linear Pair | If two angles form a linear pair, they are supplementary. | Vertical Angles | Vertical angles are congruent. | Triangle Sum | The sum of the interior angles of a triangle is 180º. | Corresponding Angles | If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. | Corresponding Angles Converse | If two lines are cut by a transversal and the corresponding angles are congruent, the lines are parallel. | Alternate Interior Angles | If two parallel
Also: Betweeness of Points: AB + BC = AC
Angle Addition Postulate: m<ABC + m<CBD = m<ABD | Construction | Two points determine a straight line. | Construction | From a given point on (or not on) a line, one and only one perpendicular can be drawn to the line. | Right Angles | All right angles are congruent. | Straight Angles | All straight angles are congruent. | Congruent Supplements | Supplements of the same angle, or congruent angles, are congruent. | Congruent Complements | Complements of the same angle, or congruent angles, are congruent. | Linear Pair | If two angles form a linear pair, they are supplementary. | Vertical Angles | Vertical angles are congruent. | Triangle Sum | The sum of the interior angles of a triangle is 180º. | Corresponding Angles | If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. | Corresponding Angles Converse | If two lines are cut by a transversal and the corresponding angles are congruent, the lines are parallel. | Alternate Interior Angles | If two parallel