# NCERT Mathematics Class 9 Exemplar Ch 8 Quadrilaterals Part 3

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**Exercise 8.2**

Q.1. Diagonals AC and BD of a parallelogram ABCD intersect each other at O. If and, determine the lengths of AC and BD.

Answer:, ; Diagonals of a parallelogram bisect each other

Q.2. Diagonals of a parallelogram are perpendicular to each other. Is this statement true? Give reason for your answer.

Answer: No; Diagonals of a parallelogram bisect each other.

Q.3. Can the angles and is the angles of a quadrilateral? Why or why not?

Answer: No; Angle sum must be 360°.

Q.4. In quadrilateral ABCD, What special name can be given to this quadrilateral?

Answer: Trapezium.

Q.5. All the angles of a quadrilateral are equal. What special name is given to this quadrilateral?

Answer: Rectangle.

Q.6. Diagonals of a rectangle are equal and perpendicular. Is this statement true? Give reason for your answer.

Answer: No; Diagonals of a rectangle need not be perpendicular.

Q.7. Can all the four angles of a quadrilateral be obtuse angles? Give reason for your answer.

Answer: No; sum of the angles of a quadrilateral is 360°.

Q.8. In ∆ ABC,, and . If D and E are respectively the mid-points of AB and BC, determine the length of DE.

Answer: , as

Q.9. In Fig, it is given that BDEF and FDCE are parallelograms. Can you say that? Why or why not?

Answer: Yes; because and.

Q.10. In Fig.8.2, ABCD and AEFG are two parallelograms. If , determine ∠F.

Answer: and