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September 1, 2014

September 1, 2014

Posted by **ujjval** on Monday, January 28, 2013 at 8:45am.

Points of AB, BC, CD and DA respectively . Show

PR and QS bisects each other.

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**Reiny**, Monday, January 28, 2013 at 9:50amAfter joining AC and using the midpoint of a triangle theorem ,it is easy to prove PQRS is a parallelogram

A property of a parallelogram is that its diagonals bisect each other.

Done.

Write it up according to the method that your instructor wants.

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**ujjval**, Monday, January 28, 2013 at 10:12amHey can u explain me more briefly

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**Reiny**, Monday, January 28, 2013 at 10:24amIt is hard for me to tell how rigorous your proof must be.

One of the features of Euclidean geometry is that it is cumulative, that is, you can use the result of one problem as a given in a new problem

To reach this point illustrated by your problem above, you must have at one time proved that :

In any triangle the line joining the midpoints of any two sides is one-half the length and parallel to the third side.

As I said, I don't know whether your method would involve simply using that result, or whether you have to actually prove that as part of the above problem. I would guess you wouldn't have to.

So you can prove that in PQRS , the opposite sides are parallel, thus making it a parallelogram.

Then by drawing diagonals of this parallelogram, you can prove triangles congruent, ASA all over the place, and thus prove the diagonals bisect each other.

(bisect means cutting into two equal parts)

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