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P,Q are the mid points of the opposite side AB and CD of a parallelogram ABCD. AP intersects DP at S and BQ intersects CP at P. Show that PQRS is a parallelogram.

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ABCD is a parallelogram in which P and Q are mid-points of opposite sides AB and CD (see Fig. 8.18). If AQ intersects DP at S and BQ intersects CP at R, show that: APCQ is a parallelogram.

ABCD is a parallelogram in which P and Q are mid-points of opposite sides AB and CD (see Fig. 8.18). If AQ intersects DP at S and BQ intersects CP at R, show that: DQBP is a parallelogram.

If P and Q are the middle points of the sides BC and CD of the parallelogram ABCD, then AP+AQ is equal to

In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP=BQ. Show that APCQ is a parallelogram.

The sides AB and CD of a parallelogram ABCD are bisects at E and F. prove that EBFD is parallelogram.

P and Q are points on opposite sides AD and BC of a parallelogram ABCD such that PQ passes through the point of intersection of its diagonals AC and BD. Show that PQ is bisected at O.

P is the mid point of side AB of a parallelogram ABCD. A line through B parallel to PD meets DC at Q and AD produced at R. prove that BR=2BQ.

P is the mid point of side AB of a parallelogram ABCD. A line through B parallel to PD meets DC at Q and AD produced at R. prove that AR=2BC.

E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that triangleABE ~ triangleCFB .

P,Q,R and S are respectively the mid points of the sides AB,BC,CD and Da of a quadrilateral ABCD in which AC=BD and ACbotBD . Prove that PQRS is a square.

MODERN PUBLICATION-QUADRILATERALS-EXERCISE
  1. P,Q are the mid points of the opposite side AB and CD of a parallelogr...

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  2. Three angles of a quadrilteral are respectively 50^@ and 110^@ and 100...

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  3. The angle of a quadrilateral are in the ratio 2: 4: 5: 7. find the ang...

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  4. In the quad. ABCD is a point inside it. Find that OA+OB+OC+OD>AC+BD.

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  5. In the fig. BLbotAC and DMbotAC. If BL=LM prove that AC bisects BD

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  6. In the fig. ABCD is a square and anglePQR=90^@ PB=QC=DR, prove that:QB...

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  7. In the fig. ABCD is a square and anglePQR=90^@ PB=QC=DR, prove that:PQ...

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  8. In the fig. ABCD is a square and anglePQR=90^@ PB=QC=DR, prove that:an...

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  9. ABCD is a quadrilateral whose diagonals AC and BD intersect at O, prov...

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  10. ABCD is a quadrilateral whose diagonals AC and BD intersect at O, prov...

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  11. A diagonal of a rectangle is inclined to one side of the rectangle at ...

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  12. In a parallelogram, prove that sum of any two consecutive angles is 18...

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  13. If an angle of a parallelogram is two thid of its adjacent angle, find...

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  14. In the fig. ABCD is a parallelogram in which angleDAB=60^@ and angleDB...

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  15. In the fig. ABCD is a parallelogram in which angleBAO=35^@, angleDAO=4...

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  16. In the fig. ABCD is a parallelogram in which angleBAO=35^@, angleDAO=4...

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  17. In the fig. ABCD is a parallelogram in which angleBAO=35^@, angleDAO=4...

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  18. In the fig. ABCD is a parallelogram in which angleBAO=35^@, angleDAO=4...

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  19. The diagonals of a rhombus are perpendicular to each other .

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  20. The diagonals of a rectangle ABCD meet at o and angleBOC=44^@ and find...

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  21. ABCD is a rectangle with angleABD=40^@ determine angleDBC.

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