# Re: geometry proof

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Posted by jacob on October 29, 2002 at 11:36:34:

In Reply to: Re: geometry proof posted by Soroban on October 29, 2002 at 11:15:33:

: : How do i write a two column proof for this problem.
: : Given: Isoceles trapezoid PQRS with bases PQ and SR
: : and diagonals SQ and PR; W, X, Y ,Z are midpoints of sides PS, PQ, QR, and RS respectively.
: : Prove: WXYZ is a rhombus.

: Hello, Jacob!

: Did you know this?
: If we connect the midpoints of the sides of ANY quadrilateral
: (even a "bent" one in 3-space), we get a parallelogram?

: In triangle PRS, X and W are midpoints of PQ and PS.
: Hence, XW || QS and XW = QS/2.

: Similarly, in triangle RQS, YZ || QS and YZ = QS/2.

: Therefore, WXYZ is a parallelogram (a pair of opposites sides
: are parallel and equal).

: Now, we must show that, say, XW = XY.
: There are many ways to accomplish this.
: For example, show that triangles PRS and QRS
: are congruent, then PR = QS.

Thanks fot the help. But how do write that answer as a proof with statements and reasons.

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