Geometry Chapter 8

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john708
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133917
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Geometry Chapter 8
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2012-02-08 23:40:23
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Geometry Chapter
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Geometry Chapter 8
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  1. Diagonal of a Polygon
    A segment that joins two nonconsecutive vertices of a polygon.
  2. Interior Angles of a Triangle
    The angles on the inside of a triangle.
  3. Exterior Angles of a Triangle
    The angles on the outside of the triangle.
  4. Theorem 8.1: POLYGON INTERIOR ANGLES THEOREM
    • The sum of the measures of the interior angles:
    • ( n - 2 ) * 180 n = number of sides in a triangle
  5. Corollary To Theorem 8.1: INTERIOR ANGLES OF A QUADRILATERAL
    The sum of the measures of the interior angles of a quadrilateral is ALWAYS 360
  6. Theorem 8.2: POLYGON EXTERIOR ANGLES THEOREM
    The sum of the measures of the exterior angles of a convex polygon is ALWAYS 360
  7. Parallelogram
    A quadrilateral with both pairs of opposite sides parallel.
  8. Theorem 8.3:
    If a quadrilateral is a parallelogram, then its opposite sides are congruent.
  9. Theorem 8.4:
    If a quadrilateral is a parallelogram, then its opposite angles are congruent.
  10. Theorem 8.5:
    If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.
  11. Theorem 8.6:
    If a quadrilateral is a parallelogram, then its diagonals bisect each other.
  12. Theorem 8.7:
    If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram
  13. Theorem 8.8:
    If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
  14. Theorem 8.9:
    If one pair of opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram.
  15. Theorem 8.10:
    If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
  16. Rhombus
    A parallelogram with four congruent sides.
  17. Rectangle
    A parallelogram with four right angles.
  18. Square
    A parallelogram with four congruent sides and four right angles.
  19. Square Corollary
    A quadrilateral is a square if and only if it is a rhombus and a rectangle.
  20. Theorem 8.11:
    A parallelogram is a rhombus if only if its diagonals are perpendicular.
  21. Theorem 8.12:
    A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles.
  22. Theorem 8.13:
    A parallelogram is a rectangle if and only if its diagonals are congruant.
  23. Trapezoid
    A quadrilateral with exactly one pair of parallel sides.
  24. Bases of a Trapezoid
    The parallel sides of a trapezoid.
  25. Base Angles of a Trapezoid
    Trapezoid has 2 pairs of base angles; each pair surrouds a base.
  26. Legs of a Trapezoid
    The non-parallel sides of a trapezoid.
  27. Isosceles Trapezoid
    Trapezoid with congruent legs.
  28. Midsegment of a Trapezoid
    Segments that connects the midpoints of the legs of a trapezoid.
  29. Kite
    Quadrilateral with 2 pairs of consecutive congruent sides ( opposite sides are not congruant )
  30. Theorem 8.14:
    If a trapezoid is isoceles, then each pair of base angles is congruant.
  31. Theorem 8.15:
    If a trapezoid has a pair of congruent base angles, then its an isoceles trapezoid.
  32. Theorem 8.16:
    A trapezoid is isosceles if and only if its diagonals are congruent.
  33. Theorem 8.17: MIDSEGMENT THEOREM FOR TRAPEZOIDS
    The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases.
  34. Theorem 8.18:
    If a quadrilateral is a kite, then its diagonals are perpendicular.
  35. Theorem 8.19:
    If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.

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