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ABCD is a rectangle in which diagonal BD...

ABCD is a rectangle in which diagonal BD bisects `angle B`. Show that ABCD is a square.

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To prove that rectangle ABCD is a square given that diagonal BD bisects angle B, we can follow these steps: ### Step 1: Draw the Rectangle Draw rectangle ABCD with vertices A, B, C, and D such that AB is parallel to CD and AD is parallel to BC. ### Step 2: Identify Angles Since ABCD is a rectangle, we know that: - Angle A = Angle B = Angle C = Angle D = 90 degrees. ...
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NCERT EXEMPLAR ENGLISH-QUADRILATERALS -LONG ANSWER TYPE QUESTIONS
  1. A square is incribed in an isoceles right triangle, so that the square...

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  2. In a parallelogram ABCD, AB = 10 cm and AD = 6 cm. The bisector of ang...

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  3. P, Q , R and S are respectively the mid-points of the sides AB, BC, C...

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  4. ABCD is a rhombus and P, Q, R and S are wthe mid-points of the side...

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  5. P, Q, R and S are respectively the mid-points of sides AB, BC, CD and ...

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  6. If diagonal of a parallelogram bisects one of the angles of the para...

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  7. ABCD is a parallelogram in which P and Q are mid-points of opposite ...

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  8. ABCD is a quadrilateral in which AB||DC and AD = BC. Prove that angleA...

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  9. In figure, AB||DE, AB=DE, AC||DF and AC=DF. Prove that BC||EF and BC=E...

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  10. In A B C ,A D is the median through A and E is the mid-point of A D ....

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  11. Show that the quadrilateral, formed by joining the mid-points of the ...

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  12. In Figure, A B C D isa trapezium in which side A B is a parallel to si...

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  13. Prove that the quadrilateral formed by the bisectors of the angles of ...

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  14. P and Q are points on opposite sides AD and BC of a parallelogram ABCD...

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  15. ABCD is a rectangle in which diagonal BD bisects angle B. Show that AB...

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  16. In DeltaA B C, D, E and F are respectively the mid-points of sides AB...

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  17. Prove that the line segment joining the mid-points of the diagonals of...

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  18. P is the mid-point of the side CD of a parallelogram ABCD. A line thro...

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