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In the alongside diagram, the bisectors ...


In the alongside diagram, the bisectors of interior angles of the parallelogram PQRS enclose a quadrilateral ABCD.
Show that:
(i) `anglePSB+angleSPB=90^(@)`
(ii) `anglePBS=90^(@)`
(iii) `angleABC=90^(@)`
(iv) `angleADC=90^(@)`
(v) `angleA=90^(@)`
(vi) ABCD is a rectangle
thus, the bisectors of the angles of a parallelogram enclose a rectangle.

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ICSE-SPECIAL TYPES OF QUADRILATERALS-EXERCISE
  1. In rhombus ABCD: (i) if angleA=74^(@), find angleB and angleC. (ii...

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  2. In square PQRS: (i) if PQ=3x-7 and QR=x+3, find PS. (ii) if PR=5x ...

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  3. ABCD is a rectangle. If angleBPC=124^(@). Calculate: (i) angleBA...

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  4. ABCD is a rhombus. If angleBAC=38^(@), find: (i) angleACB (ii) ang...

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  5. ABCD is a rhombus. If angleBCA=35^(@), and angleADC.

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  6. PQRS is a parallelogram whose diagonals intersect at M. if anglePMS=...

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  7. . Given: Parallelogram ABCD in which diagonals AC and CD intersect...

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  8. In an isosceles-trapezium, show that the opposite angles are supplemen...

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  9. ABCD is a parallelogram. What kind of quadrilateral is it if: (i) AC...

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  10. Prove that the diagonals of a parallelogram bisect each other.

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  11. If the diagonals of a parallelogram are of equal lengths, the parallel...

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  12. In parallelogram ABCD, E is the mid-point of AD and F is the mid-point...

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  13. In parallelogram ABCD, E is the mid-point of side AB and CE bisect ang...

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  14. In the alongside diagram, the bisectors of interior angles of the para...

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  15. In parallelogram ABCD, X and Y are mid-points of opposite sides AB and...

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  16. The given figure shows parallelogram ABCD. Points M and N lie in diago...

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  17. . The given figure shows a rhombus ABCD in which angle BCD=80^(@). F...

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  18. Use the information given in the following diagram to find the values ...

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  19. The following figure is a rectangle in which x:y=3:7, find the values ...

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  20. In the given figure, AB////EC,AB=AC and AE bisects angleDAC. Prove tha...

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