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Question no 5

Question no 5 ,ABCP iS a parallelograrvv I n diculars AP and BQ ave meet produced. Prove that AP — g. E and F are the mid-points of AB and mc sides of a AABC. P is any point on P.C. AP cuts EF at Q. Prove that AQ = PQ. 3. E and F are the mid-points of sides AB and CD respectively of a parallelogram ABCD prove that AEFD is a parallelogram. 4. ABCD is a parallelogram and its diagonals intersect each other at O. Through O, a straight line is drawn cutting AB in P and CD in Q. Prove that OP = QO. . Prove that in any quadrilateral, the straight lines joining the mid-points of the sides f a parallelogram. ABCD is barallelogram. The bisectors of A and C meet the diagonal BD in nd Q respectively. Prove that AAPB ACQ

Dear Student, 

We have the following situation-

Let ABCD be a quadrilateral and P,Q,R and S be the mid point of the respective sides of the triangle.

Since according to the mid point theorem, line joining the mid-points of two sides of the triangle is parallel to the third side and half of it.

In triangle ABC

Similarly in triangle ADC

Hence, opposite sides are equal and parallel.

Regards

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