remygeo - geoA - unit 3

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Author:
remygeometry
ID:
123853
Filename:
remygeo - geoA - unit 3
Updated:
2012-01-17 18:58:50
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remy geometry
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Flashcards for the theorems, postulates, and definitions of unit 3
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  1. Unique Line Postulate
    • Through any two points there is exactly one line
    • (a line is determined by two points)
  2. Postulate: If two lines intersect, then they intersect...
    ...in exactly one point
  3. Unique Plane Postulate
    • Through any three non-collinear points there is exactly one plane
    • (three noncollinear points determine a plane)
  4. Postulate: If two planes intersect, then they intersect...
    ...in exactly one line.
  5. Angle Addition Postulate
  6. Linear Pair Postulate
  7. Linear Pair Theorem
  8. Vertical Angles Theorem
    If two angles are vertical, then they are congruent.
  9. Parallel Postulate (Playfair's Axiom)
    • Through a point not on a given line, there is exactly one line parallel to the given line.
    • (Allows you to add a parallel line to a diagram)
  10. Perpendicular Postulate
    • Through a point not on a given line, there is exactly one line perpendicular to the given line.
    • (Allows you to add a perpendicular line to a diagram)
  11. Corresponding Angles Postulate
    If two parallel lines are cut by a transversal, then corresponding angles are congruent.
  12. Converse of the Corresponding Angles Postulate
    If two lines are cut by a transversal, and corresponding angles are congruent, then the lines are parallel.
  13. Alternate Interior Angles Theorem
    If two parallel lines are cut by a transversal, then alternate interior angles are congruent.
  14. Converse of the Alternate Interior Angles Theorem
    If two lines are cut by a transversal, and alternate interior angles are congruent, then the lines are parallel.
  15. Same Side Interior Angles Theorem
    If two parallel lines are cut by a transversal, then same side interior angles are supplementary angles.
  16. Converse of the Same Side Interior Angles Theorem
    If two lines are cut by a transversal, and same side interior angles are supplementary, then the lines are parallel.
  17. Triangle Angle-Sum Theorem
    The sum of the measures of the interior angles of a triangle is 180 degrees.
  18. No Choice Theorem
    If two angles of a triangle are congruent to two angles of another triangle, then the third angles are congruent.
  19. Triangle Exterior Angle Theorem
    • The measure of an exterior angle of a triangle is equal to the sum of the non-adjacent (“remote”) interior angles of the triangle.
  20. Isosceles Triangle Theorem
    • If two sides of a triangle are congruent, then the angles opposite these sides are congruent.
    • (if sides, then angles)
  21. Converse of the Isosceles Triangle Theorem
    • If two angles of a triangle are congruent, then the sides opposite the angles are congruent.
    • (if angles, then sides)
  22. Theorem: The bisector of the vertex angle of an isosceles triangle is...
    • ... the perpendicular bisector of the base.
  23. Theorem: If a triangle is equilateral, then the triangle is...
    • ...equiangular.
  24. Congruent Supplements Theorem
    If two angles are supplements of the same angle (or of congruent angles), then the two angles are congruent.
  25. Congruent Complements Theorem
    If two angles are complements of the same angle (or of congruent angles), then the two angles are congruent.
  26. Right Angle Congruence Theorem
    If two angles are right angles, then they are congruent.
  27. Angle Bisector Theorem
  28. Midpoint Theorem



  29. Segment Division Theorem
    The like divisions of congruent segments are congruent.
  30. Angle Division Theorem
    The like divisions of congruent angles are congruent.
  31. Segment Multiplication Theorem
    The like multiples of congruent segments are congruent.
  32. Angle Multiplication Theorem
    The like multiples of congruent angles are congruent.
  33. Theorem: If the exterior sides of two adjacent acute angles are perpendicular then...
    ... the angles are complementary
  34. Theorem: If two lines are perpendicular then they form...
    ...congruent adjacent angles.
  35. Theorem: If two lines form congruent adjacent angles, then they are...
    ...perpendicular.
  36. Polygon Angle-Sum Theorem
    The sum of the measures of the interior angles of an n-gon is (n - 2)180
  37. Polygon Exterior Angle-Sum Theorem
    The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360.
  38. Theorem: The number of diagonals in an n-gon is...
  39. Side-Side-Side Theorem (SSS)
    If the three sides of one triangle are congruent to the three sides of another triangle,then the two triangles are congruent.
  40. Side-Angle-Side Theorem (SAS)
    • 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
  41. Angle-Side-Angle Postulate (ASA)
    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.
  42. Theorem: All radii of a circle are...
    ...congruent.
  43. Hypotenuse-Leg Theorem (HL)
    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.
  44. Angle- Angle-Side Theorem (AAS)
    • If two angles and the non-included side of one triangle are congruent to two angles and the non-included side of another triangle, then the two triangles are congruent.
  45. Corresponding parts of congruent triangles are congruent (CPCTC)

    What it does...
    CPCTC allow us to prove that corresponding parts of congruent triangles are congruent.
  46. Corresponding parts of congruent triangles are congruent (CPCTC)

    What it does NOT do...
    CPCTC does NOT prove that triangles are congruent.
  47. Perpendicular Bisector Theorem
    • If a point is on the perpendicular bisector of a segment, then the point is equidistant from the endpoints of the segment.
  48. Converse of the Perpendicular Bisector Theorem
    • If a point is equidistant from the endpoints of a segment, then the point is on the perpendicular bisector of the segment.
  49. Theorem: If two points are equidistant from the endpoints of a segment, then the two points...
    • determine the perpendicular bisector of the segment.
  50. Angle Bisector Theorem II
    • If a point is on the bisector of an angle, then the point is equidistant from the sides of the angle.
  51. Converse of the Angle Bisector Theorem II
    • If a point in the interior of an angle is equidistant from the sides of an angle, then the point is on the angle bisector.
  52. Theorem: The perpendicular bisectors of the sides of a triangle are concurrent at a point equidistant from the...
    vertices of the triangle.
  53. Circumcenter
    The point of concurrency of the perpendicular bisectors of a triangle.
  54. Theorem: The angle bisectors of a triangle are concurrent at a point equidistant from the...
    ...sides of the triangle.
  55. Incenter
    The point of concurrency of the angle bisectors of a triangle.
  56. 3 Circumcenter Facts
    • Found using perpendicular bisectors
    • Equidistant from vertices of a triangle.
    • Is the center of circle that passes through vertices.
  57. 3 Incenter Facts
    • Found using angle bisectors
    • Equidistant from sides of a triangle
    • Is the center of circle that shares one point with each side of a triangle
  58. The circumcenter of a right triangle is always located on...
    ...the midpoint of the hypotenuse
  59. Median (of a triangle)
    A segment whose endpoints are a vertex and the midpoint of the opposite side.
  60. Centroid
    The point of concurrency of the medians of a triangle.
  61. Centroid Theorem
    The medians of a triangle are concurrent at a point that is two-thirds the distance from each vertex to the midpoint of the opposite side.
  62. Altitude (of a triangle)
    The perpendicular segment from a vertex of a triangle to the line containing the opposite side.
  63. Theorem: The lines that contain the altitudes of a triangle...
    ...are concurrent.
  64. Orthocenter
    The point of concurrency of the altitudes of a triangle.
  65. 4 Centroid Facts
    • Found using medians

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