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Transcript

1. 2. 3. 4. 5. 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.