| Term | Definition |
|---|
| Property of closure | a+b or a*b is a real number |
| Commutative property of addition | a+b=b+a |
| Associative property of addition | (a+b)+c=a+(b+c) |
| Additive identity | a+0=a, 0+a=a |
| Commutative property of multiplication | ab=ba |
| Multiplicative identity | a*1=a, 1(a)=a |
| Associative property of multiplication | (ab)c=a(bc) |
| Addition property of equality | If a=b then a+c=b+c |
| Subtraction property of equality | If a=b then a-c=b-c |
| Multiplication property of equality | If a=b then ac=bc |
| Division property of equality | If a=b and c does not equal 0 then a divided by c=b divided by c. |
| Reflexive property | For any real number, a=a. |
| Symmetric property | If a=b then b=a |
| Transitive property | If a=b and b=c then a=c |
| Substitution property | If a=b then a may be substituted for b in any equation. |
| Property of Parallel Lines | Two nonvertical lines in a plane are parallel if and only if they have the same slope. |
| Property of Perpendicular Lines | Two nonvertical lines are perpendicular if and only if the product of their slope is -1. |
| Segment Addition Postulate | If b is between a and c then ab+bc=ac. |
| Angle Addition Postulate | If b is in the interior of angle aoc then mAOC +mBOC=mAOC. |
| Linear Pair Postulate | If two angles form a linear pair then they are supplementary. |
| Parallel Postulate | If there is a line and a point not on the line, then there exactly one line through the given point parallel to the given line. |
| Perpendicular Postulate | If there is a line and a point not on the line then there is exactly one line through the given point perendicular to the given line. |
| Corresponding Angles Postulate | If two parallel lines are cut by a transversal, then the corresponding angles are congruent. |
| Corresponding Angles Converse | If two lines are cut by a transversal and the corresponding angles are congruent then the lines are parallel. |
| Congruent Supplements Theorem | If two angles are supplementary to the same angles or to congruent angles, then they are congruent. |
| Congruent Complements Theorem | If two angles are complementary to the same angle or angles, then they are congruent. |
| Vertical Angles Theorem | If two angles are vertical angles, they are congruent. |
| Transitive property of parallel lines | If two lines are parallel to the same line, then they are parallel to each other. |
| Property of Perpendicular lines | If two co-planar lines are perpendicular to the same line, then they are parallel to each other. |
| Alternate Interior angles Theorem | If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. |
| Consecutive interior angles theorem | If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary. |
| Alternate exterior angles theorem | If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent. |
| Perpendicular transversal theorem | If a transversal is perpendicular to one of two parallel lines, it is perpendicular to the second. |
| Alternate interior angles converse | If two lines are cut by a transversal so that the alternate interior angles are congruent, then the lines are parallel. |
| Consecutive interior angles converse | If two lines are cut by a transversal so that consecutive interior angles are supplementary, the lines are parallel. |
| Alternate exterior angles converse | If two lines are cut by a transversal so that alternate extreior angles are congruent, the lines are parallel. |
| Self-congruence property of triangles | Every triangle is congruent to itself. |
| Symmetric property of congruent triangles | If triangle ABC is congruent to triangle PQR then triangle PQR is congruent to triangle ABC |
| Transitive property of congruent triangles | If triangle ABC is congruent to triangle PQR and triangle PQR is congruent to triangle TUV then triangle ABC is congruent to triangle TUV. |
| Triangle Sum Theorem | The sum of the measures of the interior angles of a triangle is 180 degrees. |
| Third Angles Theorem | If two angles of a triangle are congruent to two angles of a second triangle, then the third angles are also congruent. |
| Exterior Angle Theorem | The measure of an exterior angle of a triangle is equal to the sum of the two remote angles. |
| Exterior Angle Inequality | The measure of an exterior angle of a triangle is greater than the measure of either of the two remote interior angles. |
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