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Postulate 1­1 Through any two points there is exactly one line Postulate 1­2 If two lines intersect, then they intersect in exactly one point Postulate 1­3 If two planes intersect, then they intersect in exactly one line Postulate 1­4 Through any three noncollinear points there is exactly one plane Formula The Distance Formula: The distance d between two points A(x1, y1) and B(x2, y2) is d=sqrt[(x2­x1)^2 + (y2­y1)^2] 6. Formula The Midpoint Formula: The coordinates of the midpoint M of AB with endpoints A(x1, y1) and B(x2, y2) are M=[(x1­x2)/2 , (y1­y2)/2] 7. Perimeter of Square: P=4s 8. Area of Square: A=s^2 9. Perimeter of Rectangle: P=2b+2h 10. Area of Rectangle: A=bh 11. Circumference of Circle: C=pi*d or 2pi(r) 12. Area of circle= pi(r)^2 13. Reflexive Property: segment AB is congruent to AB 14. Transitive Property: If AB is congruent to CD and CD is congruent to EF, then AB is congruent to EF 15. Theorem 2­1 Vertical Angles Theorem: vertical angles are congruent 16. Theorem 2­2 Congruent Supplements Theorem: if two angles are supplements of the same angle (or of congruent angles), then the two angles are congruent 17. Theorem 2­3 Congruent Complements Theorem: if two angles are complements of the same angle (or of congruent angles), then the two angles are congruent 18. Theorem 2­4 All right angles are congruent 19. Theorem 2­5 If two angles are congruent and supplementary, then each is a right angle 20. Postulate 3­1 Corresponding Angles Postulate: If a transversal intersects two parallel lines, then corresponding angles are congruent 21. Theorem 3­1 Alternate Interior Angles Theorem: If a transversal intersects two parallel lines, then alternate interior angles are congruent 22. Theorem 3­2 Same­Side Interior Angles Theorem: If a transversal intersects two parallel lines, then same­side interior angles are supplementary 23. Theorem 3­3 Alternate Exterior Angles Theorem: If a transversal intersects two parallel lines, then alternate exterior angles are congruent 24. Theorem 3­4 Same­Side Exterior Angles Theorem: If a transversal intersects two parallel lines, then same­side exterior angles are supplementary 25. Postulate 3­2 Converse of the Corresponding Angles Postulate: If two lines and a transversal form corresponding angles that are congruent, then the two lines are parallel 26. Theorem 3­5 Converse of the Alternate Interior Angles Theorem: If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel 27. Theorem 3­6 Converse of the Same­Side Interior Angles Theorem: If two lines and a transversal form same­side interior angles that are supplementary, then the two lines are parallel 28. Theorem 3­7 Converse of the Alternate Exterior Angles Theorem: If two lines and a transversal form alternate exterior angles that are congruent, then the two lines are parallel 29. Theorem 3­8 Converse of the Same­Side Exterior Angles Theorem: If two lines and a transversal form same­side exterior angles that are supplementary, then the two lines are parallel 30. Theorem 3­9 If two lines are parallel to the same line, then they are parallel to each other 31. Theorem 3­10 In a plane, if two lines are perpendicular to the same line, then they are parallel to each other 32. Theorem 3­11 In a plane, if a line is perpendicular to one of two parallel lines, then it is also perpendicular to the other 33. Theorem 3­12 Triangle Angle­Sum Theorem: The sum of the measures of the angles of a triangle is 180 34. Theorem 3­13 Triangle Exterior Angle Theorem: The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles 35. Theorem 3­14 Polygon Angle­Sum Theorem: The sum of the measures of the angles of an n­gon is (n­2)180 36. Theorem 3­15 Polygon Exterior Angle­Sum Theorem: The sum of the measures of the exterior angles of a polygon, one a each vertex, is 360 37. Theorem 4­1 If two angles of one triangle are congruent to two angles of another triangle then the third angles are congruent 38. Postulate 4­1 Side­Side­Side (SSS) Postulate: If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent 39. Postulate 4­2 Side­Angle­Side (SAS) Postulate: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent 40. Postulate 4­3 Angle­Side­Angle (ASA) Postulate: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent 41. Postulate 4­4 Angle­Angle­Side (AAS) Theorem: If two angles and a nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of another triangle, then the triangles are congruent. 42. Theorem 4­3 Isosceles Triangle Theorem: If two sides of a triangle are congruent, then the angles opposite those sides are congruent 43. Theorem 4­4 Converse of Isosceles Triangle Theorem: If two angles of a triangle are congruent, then the sides opposite the angles are congruent 44. Theorem 4­5 The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base 45. Corollary to Theorem 4­3: If a triangle is equilateral, then the triangle is equiangular 46. Corollary to Theorem 4­4: If a triangle is equiangular, then the triangle is equilateral 47. Theorem 4­6 Hypotenuse­Leg (HL) Theorem: If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.