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# Module 14 - 15

### This contains postulates and theorems of Module 14 - 15.1

Vertical Angles Theorem If 2 angles are vertical angles, then the angles are congruent
Transversal a line that intersects at least 2 coplanar lines at 2 different points
Corresponding angles lie on the same side of the transversal and the same side of intersected lines
Same-side interior angles lie on the same side of the transversal and between the intersected lines
Alternate interior angles nonadjacent angles that lie on the opposite sides of the transversal between the intersected lines
Alternate exterior angles lie on the opposite sides of the transversal and outside the intersected lines
Same-side interior angles postulate If 2 parallel lines are cut by a transversal then the pairs of same-side interior angles are supplementary
Alternate Interior Angles Theorem If 2 parallel lines are cut by a transversal, then the pairs of alternate interior angles have the same measure
Corresponding Angles Theorem If 2 parallel lines are cut by a transversal, then the pairs of corresponding angles have the same measure
Converse of the Same-Side Interior Angles Postulate If 2 lines are cut by a transversal of same-side interior angles are supplementary, then the lines are parallel
Converse of the Alternate Interior Angles Theorem If 2 lines are cut by a transversal so that any pair of alternate interior angles are congruent, then the lines are parallel
Converse of the Corresponding Angles Theorem If 2 lines are cut by a transversal so that any pair of corresponding angles are congruent, then the lines are parallel
The Parallel Postulate Through a point P not on line l, there is exactly one line parallel to l
Perpendicular Bisector Theorem If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment
Converse of the Perpendicular Bisector Theorem If a point is equidistant from the endpoints, then it lies on the perpendicular bisector of the segment
Triangular Sum Theorem the sum of the angle measures of a triangle is 180 degrees
Polygon Angle Sum Theorem the sum of the measures of the interior angles of a convex polygon with n sides is (n-2)(180 degrees)
Exterior Angle Theorem the measure of an exterior angle of a triangle is equal to the sum of the measures
Regular Polygon all sides are equal; all angles are equal
Isosceles triangle a triangle with at least two congruent sides
Isosceles Triangle Theorem If 2 sides of a triangle are congruent, then the two angles opposite the sides are congruent
Equilateral Triangle Theorem If a triangle is equilateral, then it is equiangular
Converse of the Equilateral Triangle Theorem If a triangle is equiangular, then it is equilateral
Triangle Inequality Theorem The sum of any two side lengths of a triangle is greater than the 3rd side length 1. AB + BC > AC 2. BC + AC > AB 3. AC + AB > BC
Side-Angle Relationships in Triangles If 2 sides of a triangle are not congruent, then the larger angle is opposite the longer side
Angle-Side Relationships in Triangles If 2 angles of a triangle are not congruent, then the longer side is opposite the larger side
Circumcenter Theorem The perpendicular bisectors of the side of a triangle intersect at a point that is equidistant from the vertices of the triangle
Created by: pandabear66*
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