Geometry Proofs (w/Pic)

If PQRS is a rectangle and M is the midpoint of RS, prove PM is congruent to QM.
P----------------Q
|\ /|
| \ / |
| \ / |
| \ / |
| \ / |
R--------M-------S
*be as explanatory as possible

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asked by HELP
  1. Well, if it is a rhombus we know all the sides are of equal length AND opposite sides are parallel.
    All we have to prove is that the corner angles are equal
    CBE=BCE given
    so
    CBE=BCE=ADE=DAE intersect parallel lines
    BE = CE isosceles
    AD = BC rhombus
    so triangle AED congruent triangle BEC from angle side angle
    triangle ABE congruent to BCE side side side
    so
    angle ABC = angle BCD= angle CDA
    4 x = 360
    x = 90 degrees

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    posted by Damon
  2. P(-3;7),Q(5;13),R(8;9) and S(0;3) are the vertices of a quadrilateral in a cartesian plane.

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    posted by Lucky
  3. Prove this P(-3;7),Q(5;13),R(8;9) and S(0;3) are the vertices of a quadrilateral in a Cartesian plane.

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    posted by Lucky

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