Properties and Postulates
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 lines are cut by...
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