| A | B |
|---|
| Reflexive Property | a = a |
| Symmetric Property | If a = b, then b = a. |
| Transitive Property | If a = b & b = c, then a = c. |
| Add/Subtract Property | If a = b, then a + c = b + c and a – c = b – c. |
| Mult/Division Property | If a = b, then ac = bc, and if c not equal to zero, a ÷ c = b ÷ c. |
| Substitution Property | If a = b, then a may be replaced by b in any equation or expression. |
| Distributive Property | a(b + c) = ab + ac |
| Supplement (or Linear Pair) Theorem | If two angles form a linear pair, then they are supplementary angles. |
| Congruent supplement Theorem | Angles supplementary to the same angle or to congruent angles are congruent. |
| Congruent Complement Theorem | Angles complementary to the same angle or to congruent angles are congruent. |
| All Right Angles = 90 | All right angles are congruent. |
| Vertical Angle Theorem (VAT) | Vertical angles are congruent. |
| Perpendicular lines form ... | four right angles. |
| Corresponding Angles Postulate (CAP) | Corresponding angles are congruent. |
| Alternate Interior Angle Theorem | Alternate interior angles are congruent. |
| Consecutive Interior Angle Theorem | Consecutive interior angles are supplementary. |
| Alternate Exterior Angle Theorem | Alternate exterior angle are congruent. |
| Perpendicular Transversal Theorem | A line perpendicular to one of two parallel lines is perpendicular to the other. |
| Alternate Interior Angle Converse | If alternate interior angles are congruent, then the two lines are parallel. |
| Consecutive Interior Angle Converse | If consecutive interior angles are supplementary, the lines are parallel. |
| Perpendicular Transversal Converse | If two lines are perpendicular to the same line, then they are parallel. |
| Parallel Lines | Two lines have the same slope |
| Perpendicular Lines | The product of their slopes is -1. |
| Corresponding Angles Converse | If corresponding angles are congruent, the lines are parallel. |
| Third Angle Theorem | If two angles of one triangle are congruent to two angles of a 2nd triangle, the 3rd angles are congruent. |
| Angle Sum Theorem | The sum of the measures of the angles of a triangle is 180. |
| Exterior Angle Theorem | The measure of an exterior angle of a triangle is equal to the sum of the two remote interior angles. |
| SSS Postulate | If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent. |
| SAS Postulate | If two sides and the INCLUDED ANGLE of one triangle are congruent to two sides and the INCLUDED angle of another triangle, then the triangles are congruent., |
| ASA Postulate | If two angles and the INCLUDED SIDE of one triangle are congruent to two angles and the INCLUDED side of another triangle, then the triangles are congruent. |
| AAS Theorem | If two angles and a NON-INCLUDED SIDE of one triangle are congruent to the corresponding two angles and side of a second triangle, the two triangles are congruent. |
| Isosceles Triangle Theorem | If two sides of a triangle are congruent, then the angles opposite those sides are congruent. |
| Converse of Isosceles Triangle Theorem | If two angles of a triangle are congruent, then the sides opposite those angles are congruent. |
| Each angle of an equilateral ∆ has a measure of | 60 degrees. |
| HL (Hypotenuse-Leg) | If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent. |
| Exterior Angle Inequality Theorem | If an angle is an exterior angle of a triangle, then its measure is greater than the measure of either of its corresponding remote interior angles. |
| If one side of a triangle is longer than another side, | then the angle opposite the longer side has a greater measure than the angle opposite |
| If one angle of a triangle has a greater measure than another angle, | then the side opposite the greater angle is longer than the side opposite the lesser angle, |
| The perpendicular segment from a point to a line | is the shortest segment from the point to the line. |
| Triangle Inequality Theorem | The sum of the lengths of any two sides of a triangle is greater than the length of the third side. |
| Definition of a Parallelogram | both pairs of opposite sides of a quadrilateral are parallel |
| If the diagonals of a parallelogram are both congruent and perpendicular, | then the parallelogram is a square |
| If the diagonals of a parallelogram are congruent, | then the parallelogram is a rectangle. |
| Definition of a Rectangle | A quadrilateral with 4 right angles. |
| If the diagonals of a parallelogram are congruent, | then the parallelogram is a rhombus. |
| Definition of a Square | A quadrilateral with 4 congruent sides and 4 right angles. |
| Definition of a Rhombus | A quadrilateral with 4 congruent sides. |
| Definition of a Trapezoid | a quadrilateral with exactly one pair of parallel sides. |
