1.) Three angles of a quadrilateral are 75º, 90º and 75º. The fourth angle is
(A) 90º
(B) 95º
(C) 105º
(D) 120º
(B) 95º
(C) 105º
(D) 120º
2. A diagonal of a rectangle is inclined to one side of the rectangle at 25º. The acute angle between the diagonals is
(A) 55º
(B) 50º
(C) 40º
(D) 25º
(B) 50º
(C) 40º
(D) 25º
3. ABCD is a rhombus such that ∠ACB = 40º. Then ∠ADB is
(A) 40º
(B) 45º
(C) 50º
(D) 60º
(B) 45º
(C) 50º
(D) 60º
Hint : Diagonal of Rhombus bisect each other at 90º.
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 sides of a 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
(B) parallelogram
(C) trapezium
(D) kite
(D) kite
Hint : Two pair of adjacent agnles are supplementary.
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
(B) rhombus
(C) parallelogram
(D) quadrilateral whose opposite angles are supplementary
8. If APB and CQD are two parallel lines, then the bisectors of the angles APQ, BPQ, CQP and PQD form
(A) a square
(B) a rhombus
(B) a rhombus
(C) a rectangle
(D) any other parallelogram
OR
(D) any other parallelogram
OR
If two parallel lines are intersected intersect by a transversal, then the bisectors of the two pairs of interior angles enclose
(a) a square
(b) a parallelogram
(c) a rectangle
(d) a trapezium
9. The figure obtained by joining the mid-points of the sides of a rhombus, taken in
order, is
(A) a rhombus
(B) a rectangle
(C) a square
(D) any parallelogram
(A) a rhombus
(B) a rectangle
(C) a square
(D) any parallelogram
Hint : Check Question No. 4.
10. D and E are the mid-points of the sides AB and AC of ∆ABC and O is any point on
side BC. O is joined to A. If P and Q are the mid-points of OB and OC respectively,
then DEQP is
(A) a square
(B) a rectangle
(C) a rhombus
(D) a parallelogram
(A) a square
(B) a rectangle
(C) a rhombus
(D) a parallelogram
Hint : If one pair of opposite sides of a quadrilateral in equal and parallel then it is a _________.
11. The figure formed by joining the mid-points of the sides of a quadrilateral ABCD, taken in order, is a square only if,
(A) ABCD is a rhombus
(B) diagonals of ABCD are equal
(C) diagonals of ABCD are equal and perpendicular
(D) diagonals of ABCD are perpendicular.
Hint : Check Question No. 5.
12. The diagonals AC and BD of a parallelogram ABCD intersect each other at the
point O. If ∠DAC = 32º and ∠AOB = 70º, then ∠DBC is equal to
(A) 24º
(B) 86º
(C) 38º
(D) 32º
(B) 86º
(C) 38º
(D) 32º
Hint : Use the concept of alternate interior angles, linear pair and angle sum property.
13.Which of the following is not true for a parallelogram?
(A) opposite sides are equal
(B) opposite angles are equal
(C) opposite angles are bisected by the diagonals
(D) diagonals bisect each other.
Answer Key
1. (D) 120º
2. (B) 50º
3. (C) 50º
4. (C) diagonals of PQRS are perpendicular
5. (D) diagonals of PQRS are equal.
6. (C) trapezium
7. (D) quadrilateral whose opposite angles are supplementary
8. (C) a rectangle or (c) a rectangle
9. (B) a rectangle
10. (D) a parallelogram
10. (D) a parallelogram
11. (C) diagonals of ABCD are equal and perpendicular
12. (C) 38º
13. (C) opposite angles are bisected by the diagonals