Postulates+and+Theorems

Postulates and Theorems
 * Right Angle Congruence Postulate: All right angles are congruent
 * Vertical Angles Congruence Theorem: Vertical angles are congruent
 * Congruent Complements Theorem: If two angles are complementary to the same angle then they are congruent.
 * Congruent Complements Theorem: If two angles are supplementary to the same angle then they are congruent.
 * Ruler Postulate: Points on a line can be matched on the line with real numbers. The real numbers are called coordinates.
 * Segment Addition Postulate: If B is between A and C then AB+BC=AC.
 * Angle Addition Postulate: If P is in the interior of <RST then the measures of <RSP and <PST will equal the measure of <RST. <RSP+<PST=<RST
 * Postulate 5: Through any two points there exists exactly one line.
 * Postulate 6: A line contains at least two points.
 * Postulate 7: If two lines intersect then their intersection is exactly one point.
 * Postulate 8: Through any three noncollinear points there exists exactly one plane.
 * Postulate 9: A plane contains at least 3 noncollinear points.
 * Postulate 10: If two points lie in a plane then the line containing them is in the plane.
 * Postulate 11: If two planes intersect then their intersection is a line.
 * 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 is exactly one line through the point parallel to the line.
 * Perpendicular Postulate: If there is a line and a point not on the line then there is exactly one line through the point perpendicular to the line.
 * Alternate Interior Angles Theorem: If two parallel lines are cut by a transversal then the pairs of alternate exterior angles are congruent.
 * Alternate Exterior Angles Theorem: If two parallel lines are cut by a transversal then the pairs of alternate exterior 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.
 * Corresponding Angles Postulate: If two parallel lines are cut by a transversal then their corresponding angles are congruent.
 * Alternate Interior Angles Converse: If two lines are cut by a transversal so the alternate interior angles are congruent their lines are parallel.
 * Alternate Exterior Angles Converse: If two lines are cut by a transversal so the alternate exterior angles are congruent then the lines are parallel.
 * Consecutive Interior Angles Converse: If two lines are cut by a transversal so the consecutive interior angles are supplementary then the lines are parallel.
 * Theorem 3.8- If two lines intersect to form a linear of congruent angles then the lines are perpendicular.
 * Theorem 3.9- If two lines are perpendicular then they intersect to form four right angles.
 * Theorem 3.10- If two sides of two adjacent acute angles are perpendicular then the angles are complementary.
 * Perpendicular Transversal Theorem- If a transversal is perpendicular to one of two parallel lines then it is perpendicular to the same line then they are parallel to the other.
 * Lines perpendicular to a transversal theorem- In a plane, if two lines are perpendicular to the same line then they are parallel to each other.
 * Triangle sum theorem- The sums of the interior angles of triangles 180 degrees.
 * Exterior angle theorem- To measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.
 * Corollary to the triangle sum theorem- The acute angles of a right triangle are complementary.
 * Third angles theorem- If two angles are congruent to two angles of another triangle then the third angles are also congruent.SSS
 * SSS Congruence Postulate: If three side of one triangle are congruent to three sides of a second triangle then the two triangle are congruent.
 * SAS Congruence Postulate- If two sides and the included angle of a second triangle then the two triangles are congruent.
 * HL Congruence Theorem- If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle then the two triangles are congruent.
 * ASA Congruence Postulate- If two angles and the included side of one triangle are congruent to two angles and he included side of a second triangle then the two triangles are congruent.
 * AAS Congruence Theorem- If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle then the two triangles are congruent.
 * Base Angle Theorem- If two sides of a triangle are congruent the the angles opposite of them are congruent.
 * Converse of Base Angles Theorem- If two angles of a triangle are congruent then the sides opposite to them are congruent.
 * Corollary to the Base Angles Theorem- If a triangle is equilateral then it is equiangular.
 * Corollary to the Converse of the Base Angles Theorem- If a triangle is equiangular then it is equilateral.
 * The Midsegment Theorem- The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long as that side.
 * Perpendicular Bisector- In a plane, 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- In a plane, if a point is equidistant from the endpoint of a segment then it is on the perpendicular bisector of the segment.
 * Concurrency of Perpendicular Bisector Theorem- The perpendicular bisectors of a triangle intersect at a point that is equidistant from the vertices of the triangle.
 * Angle Bisector Theorem- If a point is on the bisector of an angle then it is equidistant from the two sides of the angle.
 * Converse of the angle Bisector Theorem- If a point is in the interior of an angle and is equidistant from the sides of an angle then sides of an angle and is equidistant from the sides of an angle then it lies on the bisector of an angle.
 * Angle Angle Similarity Postulate- If two angles of one triangle are congruent to two angles of another triangle the two triangles are similar.
 * Triangle Proportionality Theorem- If a line parallel to one side of a triangle intersects the other two sides then it divides the two sides proportionality.
 * Converse of the Triangle Proportionality Theorem- If a line divides 2 sides of a triangle proportionally, then it is parallel to the 3rd side.
 * Triangle Inequality Theorem- The sum of 2 sides of a triangle is greater than the third side.
 * Pythagorean Theorem- a squared plus b squared equals c squared.
 * Converse of the Pythagorean Theorem- If the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other 2 sides, then the triangle is a right triangle.