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Geometry Theorems List

Geometry Theorems List:

Here are the List of Geometry Theorems , given below

  1. If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.
  2. In a plane, if two lines are perpendicular to the same line, then they are parallel to each other
  3. If two angles form a linear pair, then they are supplementary angles.-Supplementary theorem.
  4. If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent.
  5. If two sides of two adjacent acute angles are perpendicular,then the angles are complementary.
  6. There is  no common sides of two adjacent angles, then the angles are called complementary angles. - Complementary angles:
  7. If two lines are perpendicular, then they intersect to form four right angles.
  8. f two lines are parallel to the same line, then they are parallel to each other
  9. f two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel.
  10. Alternate Interior Angles:If two parallel lines are cut by a transversal, then the pairs of  alternate interior angles are congruent.
  11. Consecutive Interior Angles: If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary
  12. If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel
  13. The sum of the measures of the interior angles of a triangle is180o -  Triangle Sum Theorem
  14. The acute angles of a right triangle are complementary. -Corollary Theorem
  15. The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles-Exterior angle Theorem
  16. If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.-third angle theorem
  17. If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle. -Angle Bisector Theorem
  18. f a point is on a perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.- Perpendicular Bisector Theorem.
  19. 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. - Angle Angle Side Congruence Theorem
  20. 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
  21. 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
  22. 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.
  23. 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
  24. 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.

  25. Theorem based on Quadrilaterals:

  26. If an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram.
  27. If one pair of opposite sides of a quadrilateral is congruent and parallel, then the quadrilateral is a parallelogram.
  28. If a quadrilateral is a parallelogram, then its opposite angles are congruent.
  29. If a quadrilateral is a parallelogram, then its opposite sides are congruent.
  30. The sum of the measures of the interior angles of a quadrilateral is 360ยบ.
  31. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram
  32. If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.
  33. If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram
  34. If a quadrilateral is a parallelogram, then its diagonals bisect each other.
  35. 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
  36. The mid segment of a trapezoid is parallel to each base, and its length isone half the sum of the lengths of the bases.