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NCERT Mathematics Class 9 Exemplar Ch 8 Quadrilaterals Part 3
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 360Β°.
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 360Β°.
Q.8. In β 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 β F.
Answer: and