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In quadrilateral ABCD, diagonals AC and ...

In quadrilateral ABCD, diagonals AC and BD intersect at point E such that
`AE : EC = BE : ED`.
Show that : ABCD is a trapezium. 

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The diagonals of a quadrilateral ABCD intersect each other at the point O such that (A O)/(B O)=(C O)/(D O) . Show that ABCD is a trapezium.

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ICSE-SIMILARITY (WITH APPLICATIONS TO MAPS AND MODELS)-EXERCISE 15(A)
  1. Given : RS and PT are altitudes of DeltaPQR. Prove that: PQ xx QS = ...

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  2. Given : ABCD is a rhombus, DPR and CBR are straight lines. Pro...

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  3. Given : FB = FD, AE | FD and FC | AD.   Prove that: : (FB)/(AD) = (BC...

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  4. In DeltaPQR, /Q = 90^@ and QM is perpendicular to PR. Prove that : P...

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  5. In DeltaPQR, /Q = 90^@ and QM is perpendicular to PR. Prove that : Q...

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  6. In DeltaPQR, /Q = 90^@ and QM is perpendicular to PR. Prove that : P...

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  7. In Delta ABC, /B = 90^@ and BD | AC. If CD = 10 cm and BD = 8 cm, fi...

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  8. In Delta ABC, /B = 90^@ and BD | AC. If AC = 18 cm and AD = 6 cm, fi...

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  9. In Delta ABC, /B = 90^@ and BD | AC. If AC = 9 cm and AB = 7 cm, fin...

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  10. In the figure, PQRS is a parallelogram with PQ = 16 cm and QR = 10 cm....

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  11. In quadrilateral ABCD, diagonals AC and BD intersect at point E such t...

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  12. In triangle ABC, AD is perpendicular to side BC and AD^2 = BD xx DC. ...

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  13. In the given figure, AB////EF////DC, AB = 67.5 cm, DC = 40.5 cm and AE...

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  14. In the given figure, AB////EF////DC, AB = 67.5 cm, DC = 40.5 cm and AE...

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  15. In the given figure, QR is parallel to AB and DR is parallel to QB. ...

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  16. Through the mid-point M of the side C D of a parallelogram A B C D , t...

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  17. In the given figure, P is a point on AB such that AP : PB = 4: 3. PQ i...

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  18. In the given figure, P is a point on AB such that AP : PB = 4: 3. PQ i...

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  19. In the right-angled triangle QPR, PM altitude. Given that QR = 8 c...

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  20. In the figure, given below, the medians BD and CE of a triangle ABC me...

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