Prove that lines formed by joining the mid-points of the parallel sides of a rectangle bisect each-other and are perpendicular
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It's impossible to answer this without knowing what postulates and previously proved theorems you have available.
is there a postulate/theorem which says if two angles of a quadrilateral are right then the quadrilateral is rectangle?
assume any postulate/theorem (but please try to make it simple)
You wont find it difficult to draw a quadrilateral which has 2 right angles and is not a rectangle.
Euclid knew about triangles. You might want to draw the diagonal lines that connect the midpoints of the sides, and see what you can prove about the resulting triangles.
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