theorem 30

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8 Terms

1
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theorem 30

A quadrilateral is a parallelogram if its diagonals bisect each other

2
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  1. Because AC and BD bisects each other, AE = EC and BE = ED

a line segment that is bisected is divided into two equal parts

3
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  1. Angle 1 = Angle 2

Definition of vertical angles

4
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  1. Triangle AEB is congruent to Triangle CED

S.A.S

5
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AB = CD and Angle 3 = Angle 4

Corresponding parts of congruent triangles are equal

6
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AB || CD

Equal alternate interior angles mean that lines are parallel

7
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ABCD is a parallelogram

a quadrilateral is a parallelogram if two opposite sides are both parallel and equal

8
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Given

AB and CD bisect each other