Question no 4

Question no 4 ARNq MS NQ In the quadrilateral SMQN, since each = NS and MS = NQ, therefore SMq EXERCISE II(A) ABCD iS a parallelogram. From A and B perpendiculaß AP and BQ are drawn to meet CD or CD produced. Prove that AP = BQ. 2. E and F are the mid-points of AB and AC two sides of a AABC. P is any point on BC. 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. . 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 8. 9. 11

in parallelogram ABCD
take triangle ABC
we know that O is the mid point of AC therefore
by mid point theorem P is the mid point of AB
there fore AP=PB
SIMILARLY Q is the mid point of DC
therefore DQ=QC
since AB=DC
AP=PB=DQ=QC
in triangle AOP and COQ
OA =OC .......{ O is the midpoint of AC }
AP=QC........{PROVED ABOVE}
<OAP=<OCQ.....[ALT INT ANG] by SAS congruence the triangles are congruent
by CPCT OP=OQ

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