# Quadrilaterals| NCERT Solutions| Class 9

NCERT Solutions of Chapter: Quadrilateral. NCERT Solutions along with worksheets and notes for Class 9.

Exercise 8.1

(1) The angles of quadrilateral are the ratio 3: 5: 9: 13. Find all the angles of the quadrilateral.

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(2) If the diagonals of a parallelogram are equal, then show that it is a rectangle.

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(3) Show that if the diagonals of quadrilateral bisect each other at right angles, then it is a rhombus.

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(4) Show that the diagonals of a square are equal and bisect each other at right angles.

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(5) Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.

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(ii)

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(2) ABCD is a rhombus and P, Q, R and S are mid – points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rectangle.

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(3) ABCD is a rectangle and P, Q R and S are mid – points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.

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(5) In a parallelogram ABCD, E and F are the mid – points of sides AB and CD respectively (Fig. below). Show that the line segments AF and EC trisect the diagonal BD.

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(6) Show that the line segments joining the mid – points of the opposite sides of a quadrilateral bisect each other.

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Helping Topics