## Ch. 6 theorems

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spazz444  on November 17, 2011

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# Ch. 6 theorems

 Theorem 6-1opposite sides of a parallelogram are congruent
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#### Definitions

Theorem 6-1 opposite sides of a parallelogram are congruent
Theorem 6-2 opposite angles of a parallelogram are congruent
Theorem 6-3 the diagonals of a parallelogram bisect each other
Theorem 6-4 if three (or more) parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal
Theorem 6-5 if both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram
Theorem 6-6 if both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram
Theorem 6-7 If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram
Theorem 6-8 if one pair of opposite sides of a quadrilateral is both congruent and parallel then the quadrilateral is a parallelogram
Theorem 6-9 Each diagonal of a rhombus bisects two angles of the rhombus.
Theorem 6-10 The diagonals of a rhombus are perpendicular
Theorem 6-11 the diagonals of a rectangle are congruent
Theorem 6-12 If one diagonal of a parallelogram bisects two angles of the parallelogram, then the parallelogram is a rhombus.
Theorem 6-13 If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.
Theorem 6-14 If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.
Theorem 6-15 The base angles of an isosceles trapezoid are congruent.b
Theorem 6-16 The diagonals of an isosceles trapezoid are congruent.
Theorem 6-17 The diagonals of a kite are perpendicular.
Theorem 6-18 1) the midsegment of a trapezoid is parallel to the bases
2) the length of the midsegment of a trapezoid is half the sum of the lengths of the bases

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