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SAI INTERNATIONAL SCHOOL

Sub: Mathematics Class X

Worksheet-1

Ch-8 Quadrilaterals

1. Three angles of a quadrilateral are 75°, 90° and 75°, then the fourth angle is
(a) 90° (b) 95° (c) 105° (d) 120°
2. A diagonal of a rectangle is inclined to one side of the rectangle at 25°. The acute
angle between the diagonals is
(a) 55° (b) 50° (c) 40° (d) 25°
3. ABCD is a rhombus such that ∠ACB = 40°, then ∠ADB is
(a) 40° (b) 45° (c) 50° (d) 60°
4. The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS,
taken in order, is a rectangle, if
(a) PQRS is a rectangle (b) PQRS is a parallelogram
(c) diagonals of PQRS are perpendicular (d) diagonals of PQRS are equal
5. The quadrilateral formed by joining the mid-points of the side of quadrilateral PQRS, taken
in order, is a rhombus, if
(a) PQRS is a rhombus (b) PQRS is a parallelogram
(c) diagonals of PQRS are perpendicular (d) diagonals of PQRS are equal
6. If angles A, B,C and D of the quadrilateral ABCD, taken in order are in the ratio 3 :7:6:4,
then ABCD is a
(a) rhombus (b) parallelogram
(c) trapezium (d) kite
7. If bisectors of ∠A and ∠B of a quadrilateral ABCD intersect each other at P, of ∠B and ∠C
at Q, of ∠C and ∠D at R and of ∠D and ∠A at S, then PQRS is a
(a) rectangle (b) rhombus
(c) parallelogram (d) quadrilateral whose opposite angles are supplementary
8. Diagonals AC and BD of a parallelogram ABCD intersect each other at O. If OA = 3 cm
and OD = 2 cm, determine the lengths of AC and BD.
9. Diagonals of a parallelogram are perpendicular to each other. Is this statement true? Give
reason for your answer.
10. Can the angles 110°, 80°, 70° and 95° be the angles of a quadrilateral? Why or why not?
11. In figure PQRS is a parallelogram, PQ and QO are respectively, the angle bisectors of
P and Q. Line LOM is drawn parallel to PQ. Prove that (i) PL = QM
(ii) LO = OM.

12. Let ABC be an isosceles triangle with AB = AC and let D, E, F be the mid-points of BC,