If PQRS is a rectangle and M is the midpoint of RS, prove PM is congruent to QM.

Question

P----------------Q
|\ /|
| \ / |
| \ / |
| \ / |
| \ / |
R--------M-------S
*be as explanatory as possible

Answer 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

Answer 2

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

Answer 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.