![]() If three or more parallel lines intersect two transversals, then they divide the transversals proportionally. In a coordinate plane, two nonvertical lines are perpendicular IFF the product of their slopes is -1. If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment If a point is the same distance from both the endpoints of a segment, then it lies on the perpendicular bisector of the segment In a coordinate plane, two nonvertical lines are parallel IFF they have the same slope. Perpendicular Bisector Theorem Converse of the Perpendicular Bisector Theorem Parallel Lines Theorem Perpendicular Lines Theorem Two-Transversals Proportionality Corollary If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other one. Converse of Alternate If two lines are intersected by a transversal Interior Angles and alternate interior angles are equal in Theorem measure, then the lines are parallel Converse of Alternate If two lines are intersected by a transversal Exterior Angles and alternate exterior angles are equal in Theorem measure, then the lines are parallel Converse of Same-side If two lines are intersected by a transversal Interior Angles and same-side interior angles are Theorem supplementary, then the lines are parallel Theorem If two intersecting lines form a linear pair of congruent angles, then the lines are perpendicular Theorem If two lines are perpendicular to the same transversal, then they are parallel Perpendicular Transversal Theorem ![]() Lines Postulates And Theorems Name Definition Postulate Through a point not on a given line, there is one and only one line parallel to the given line Alternate Interior If two parallel lines are intersected by a Angles Theorem transversal, then alternate interior angles are equal in measure Alternate Exterior If two parallel lines are intersected by a Angles Theorem transversal, then alternate exterior angles are equal in measure Same-side Interior If two parallel lines are intersected by a Angles Theorem transversal, then same-side interior angles are supplementary. Given collinear points A,B,C and D arranged as shown, if A B ≅ C D then AC ≅ BC If two parallel lines are intersected by a transversal, then the corresponding angles are equal in measure If two lines are intersected by a transversal and corresponding angles are equal in measure, then the lines are parallel of 11Ĭorresponding Angles Postulate Converse of Corresponding Angles Postulate Lines Postulates And Theorems Name Definition Visual Clue Segment Addition For any segment, the measure of the whole postulate is equal to the sum of the measures of its non-overlapping parts Postulate Through any two points there is exactly one line Postulate Common Segments Theorem If two lines intersect, then they intersect at exactly one point. Interior of an angle is Angle Bisector equidistant from the sides of the angle, then Theorem it is on the bisector of the angle. Angle Bisector If a point is on the bisector of an angle, then Theorem it is equidistant from the sides of the angle. Congruence Theorem Vertical Angles Vertical angles are equal in measure Theorem Theorem If two congruent angles are supplementary, then each is a right angle. theorem Right Angle All right angles are congruent. Congruent If two angles are complements of the same complements angle, then they are congruent. Congruent If two angles are supplements of the same supplements theorem angle, then they are congruent. If a = b and b = c then a = c a(b + c) = ab + acĬongruence Postulates Name Definition Reflexive Property of Congruence A ≅ A Symmetric Property of If A ≅ B, then B ≅ A Congruence Transitive Property of Congruence If A ≅ B and B ≅ C then A≅C of 11Īngle Postulates And Theorems Name Definition Angle Addition For any angle, the measure of the whole is postulate equal to the sum of the measures of its nonoverlapping parts Linear Pair Theorem If two angles form a linear pair, then they are supplementary. Of equality Transitive Property of Equality Distributive Propertyĭefinition If the same number is added to equal numbers, then the sums are equal If the same number is subtracted from equal numbers, then the differences are equal If equal numbers are multiplied by the same number, then the products are equal If equal numbers are divided by the same number, then the quotients are equal A number is equal to itself If a = b then b = a If values are equal, then one value may be substituted for the other. Of equality Symmetric Property of Equality Substitution Prop.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |