Geometry Parallel Lines Planes Chap 3

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  1. Parallel Lines - coplanar lines that don't intersect
  2. Skew Lines - non-coplanar lines that don't intersect
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  3. Parallel planes - planes that don't intersect

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  4. Transversal- a line that intersects two or more coplanar lines at different points
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  5. Alternate exterior angles 

    *  If the the alternate exterior angles are congruent, then the lines are parallel.


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  6. *  If two parallel lines, then the alternate interior lines are congruent.

    *  If the alternate interior angles are congruent, then the lines are parallel.

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  7. Corresponding angles 
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  8. *  If two parallel lines, then the corresponding angles are congruent. 

    *  If the corresponding angles are congruent, then the lines are parallel.

    *  Corresponding angles are congruent.

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  9. *  If two parallel lines, then the SS-Int angles are supplementary.

    *  If the SS-Int angles are supplementary then the lines are parallel.

    *  Same Side Interior angles are supplementary (180°)

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  10. If two parallel lines, then the alternate exterior angles are congruent.

    Alternate exterior angles are congruent
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  11. If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other

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  12. In a plane if two lines are perpendicular to the same line then the lines are parallel
  13. In two lines are parallel to the same line then the lines are parallel
  14. Through a point outside a line there is exactly one line parallel or perpendicular to the given line
  15. Angle Sum Theorem

    the sum of the angles of a triangle is 180 degrees

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  16. Corollaries- statement easily proven by applying a theorem
  17. Third Angle Theorem

    If two angles in one triangle are congruent to two angles in another triangle then the third angles are congruent.

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  18. The acute angles of a right triangle are complementary (90°)

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  19. Classifying Triangles by SIDES:

    Scalene: no equal sides, no equal angles
    Isosceles: two equal sides, two equal angles
    Equilateral: three equal sides, three equal angles always 60°
  20. Scalene: no equal sides, no equal angles

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  21. Isosceles- two equal sides, two equal angles
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  22. Equilateral- three equal sides, three equal angles always 60°

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  23. Classifying triangles by ANGLES:

    * Right triangle has a right angle (90°)
    * Acute triangle all angles are less than 90°
    * Obtuse triangle has an angle more than 90°
    * Equiangular triangle has all angles measuring 60°.
  24. Right triangle has a right angle (90°).
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  25. Acute triangles: all angles are less than 90°Image Upload
  26. Obtuse triangle has an angle more than 90°.
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  27. Equiangular

    Each angle in a equiangular triangle is 60°.

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  28. There can be at most one right angle or obtuse angle in a triangle
  29. Exterior angle of triangle- an angle that forms a linear pair with an interior angle of a triangle
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  30. remote interior angles- the two angles in the triangle that are non-adjacent to the exterior angle

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  31. Exterior Angle Theorem- the measure of the exterior angle of a triangle is equal to the sum remote interior angles.
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  32. polygon

    *  2 dimensional
    *  only segments
    *  intersects at end points
  33. convex
    *  lines contain closed sides
    *  dont contain points

    non-convex
    *  concave

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  34. 3 sides --- triangle
    4 sides --- quadrilateral
    5 sides --- pentagon
    6 sides --- hexagon
    7 sides --- hectoton
    8 sides --- octagon
    9 sides --- nonagon
    10 sides -- decagon
    n sides --- whatever number of sides
  35. regular polygon

    *  equilateral and equilangular  
    *  congruent sides and all angles are congruent
  36. diagonal- a segment joining non-consecutive vertices of the polygon
  37. Interior Angle Sum Theorem

    the sum of the interior angles of a convex polygon- interior angle sum is (n-2)180


  38. To find interior angle in regular octagon.

    Interior angle = (n-2)180/n
  39. Exterior Angle Sum Theorem

    the sum of the exterior angles,  one angle at each vertex, of a convex polygon is always 360°.
  40. each exterior angle = 360/n
Author:
Mamadams
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Card Set:
Geometry Parallel Lines Planes Chap 3
Updated:
2014-12-06 22:38:05
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