math postulates,theorems, and properties
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33 terms
Terms | Definitions |
|---|---|
 Angle Addition Postulate | if point B is in the interior of <AOC the m<AOB + m<BOC = m<AOC. |
| Corresponding Angles Postualte | If a transveral intersects two parallel lines then corresponding angles are congruent. |
| Converse of the Corresponding Angles postulate | If two lines and a transveral form corresponding angles that are congruent then the two lines are parallel. |
| Addition property of Equality | If a=b the a+c = b+c |
| Subtraction Property of Equality | If a=b then a-c = b-c |
| Multiplication Property of Equality | If a=b then a X c = b X c |
| Division Property of Equality | If a=b then a/c = b/c |
| Reflexive Property of Equality | A=A (everything is equal to itself) |
| Symmetric Property of Equality | If a=b then b=a |
| Transitive Property of Equality | If a=b and b=c then a=c |
| Substitution Property of Equality | If a=b then b can replace a in any expression. |
| The Distributive Property | a(b+c) = a X b + b X c |
| Reflexive Property of Congruence | AB =~ AB <A =~ A |
| Symmetric Property of Congruence | AB =~ CD then CD =~ AB <A =~ <B then <B =~ <A |
| Transitive Property of Congruence | If <A =~ <B and <B =~ <C then <A =~ <C |
| Vertical Angles Theorem | Vertical angles are congruent. |
| Congruent Supplements Theorem | If two angles are supplementary of the same angle (or congruent angles) then the angles are congruent. |
| Congruent Complements Theorem | If two angles are complements of the same angle (or congruent angles) thn the two angles are congruent. |
| Theorem 2-4 (right angles) | All right angles are congruent. |
| Theorem 2-5 | If two angles are congruent and supplementary then each is a right angle. |
| Alternate Interior Angles Theorem | If a transversal intersects two parallel lines then alternate interior angles are congruent. |
| Same Side Interior Angles Theorem | If a transversal intersects two parallel lines the same side interior angles are supplementary. |
| Alternate Exterior Angles Theorem | If a transversal intersects two parallel lines the alternate exterior angles are congruent. |
| Same Side Exterior Angles Theorem | If a transversal intersects two parallel liknes then same side exterior angles are congruent. |
| Converse of Alternate Interior Angles Theorem | If two lines and a transversal form alternate exterior angles that are congruent then the two lines are parallel. |
| Converse of the same Side Interior Angles Theorem | If two lines and a transversal form same side interior angles that are supplementary the two lines are parallel. |
| Converse of Alternate Exterior Angles Theorem | If two lines and a transversal for alternate exterior angles that are congruent then the lines are parallel. |
| Converse of the same side exterior Angles Theorem | If two lines and a transveral form same side exterior angles that are supplementary the lines are parallel. |
| Theorem 3-9 | If two lines are parallel to the same line then they are parallel to eachother. |
| Theorem 3-10 | In a plane if two lines are perpendicular to the same line then they are parallel to eachother. |
| Theorem 3-11 | In a plane if a line is perpendicular to one of two parallel lines then it is perpendicular to the other. |
| Triangle Angle Angle Sum theorem | The sum of the measures of the angles of a triangle is 180. |
| Triangle Exterior angle Theorem | The measure of each exterior angle of a triangle equals the sum of the measures of each of its remote interior angles. |
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