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If the diagonals of a quadrilateral bise...

If the diagonals of a quadrilateral bisect each other at right angle, prove that the quadrilateral is a rhombus.
A rhombus has all its four sides equal.

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NAGEEN PRAKASHAN ENGLISH-TRIANGLES-Exercise 7a
  1. The following figure shows a square ABCD and an equilateral triangle D...

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  2. The given figure shows a parallelogram ABCD. Squares ABPQ and ADRS are...

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  3. In a Delta ABC, BD is the median to the side AC, BD is produced to E s...

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  4. In the given figure, angleBDC=angleBEA and AB = BC. Show that AE=CD.

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  5. If the diagonals of a quadrilateral bisect each other at right angle, ...

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  6. In the adjoining figure, BM and DN are the perpendiculars from B and D...

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  7. In the adjoining figure, AB=EF, BC=DE, angleABC=angleFED=90^(@), prove...

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  8. In the adjoining figure, ABCD is a parallelogram. If angleMBC = angleN...

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  9. In the adjoining figure, QX and RX are the bisectors of the angles Q a...

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  10. In the following figure, OA = OC and AB = BC. Prove that : (i) angle...

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  11. In the adjoining figure, ABCD is a paralogram. The side AB is produced...

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  12. In the following figures, AB=PQ, AC=PR and AM=PN. Prove that DeltaABC ...

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  13. Prove that the medians of an equilateral triangle are equal.

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  14. ABCD is a square EF is parallel to BD. R is the mid-point of EF. Prove...

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  15. The following figure shows a triangle ABC in which AB = AC. M is a poi...

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  16. In the given figure, AB"||"DC and angleD=angleC. Prove that : (i) AD...

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  17. In the given figure : AB//FD, AC//GE and BD = CE, prove that : (i) B...

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  18. In the adjoining figure, angleAYZ=angleBYX=90^(@), AY = YZ and XY = BY...

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  19. In the adjoining figure, ABCD is a square and PAB is an equilateral tr...

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  20. In the adjoining figure, DeltaABC is right angled at C and M is the mi...

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