Properties and Postulates

Topics: Angle, Addition, Transitive relation Pages: 2 (468 words) Published: January 15, 2013
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 lines are cut by...
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