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Geometry Theorems List
Geometry Theorems List:Here are the List of Geometry Theorems , given below
 If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.
 In a plane, if two lines are perpendicular to the same line, then they are parallel to each other
 If two angles form a linear pair, then they are supplementary angles.Supplementary theorem.
 If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent.
 If two sides of two adjacent acute angles are perpendicular,then the angles are complementary.
 There is no common sides of two adjacent angles, then the angles are called complementary angles.  Complementary angles:
 If two lines are perpendicular, then they intersect to form four right angles.
 f two lines are parallel to the same line, then they are parallel to each other
 f two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel.
 Alternate Interior Angles:If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.
 Consecutive Interior Angles: If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary
 If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel
 The sum of the measures of the interior angles of a triangle is180o  Triangle Sum Theorem
 The acute angles of a right triangle are complementary. Corollary Theorem
 The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior anglesExterior angle Theorem
 If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.third angle theorem
 If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle. Angle Bisector Theorem
 f a point is on a perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. Perpendicular Bisector Theorem.
 If two angles and a nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of a second triangle, then the two triangles are congruent.  Angle Angle Side Congruence Theorem
 If two sides of a triangle are congruent, then the angles opposite them are congruent Corollary: If a triangle is equilateral, then it is equiangular. Base Angle Theorem
 If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and leg of a second right triangle, then the two triangles are congruent.  Right angle Theorem
 If one side of a triangle is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side.
 If one angle of a triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle
 If two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first is longer than the third side of the second. Hinge Theorem.
 If an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram.
 If one pair of opposite sides of a quadrilateral is congruent and parallel, then the quadrilateral is a parallelogram.
 If a quadrilateral is a parallelogram, then its opposite angles are congruent.
 If a quadrilateral is a parallelogram, then its opposite sides are congruent.
 The sum of the measures of the interior angles of a quadrilateral is 360ยบ.
 If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram
 If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.
 If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram
 If a quadrilateral is a parallelogram, then its diagonals bisect each other.
 The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long.  Mid Segment Theorem
 The mid segment of a trapezoid is parallel to each base, and its length isone half the sum of the lengths of the bases.
Theorem based on Quadrilaterals: