8. Quadrilaterals Class 9 Mathematics NCERT Exemplar Solutions (CBSE)

Chapter 8: Quadrilaterals – Class 9 Mathematics NCERT Exemplar Solutions (CBSE Board)

Chapter 8: Quadrilaterals

EXERCISE 8.1
Write the correct answer in each of the following:
1. Three angles of a quadrilateral are 75°, 90° and 75°. 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 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
(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. 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
(C) a rectangle (D) any other parallelogram
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
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
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.
12. The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O. If ∠DAC = 32° and ∠AOB = 70°, then ∠DBC is equal to
(A) 24° (B) 86° (C) 38° (D) 32°
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.
14. D and E are the mid-points of the sides AB and AC respectively of ∆ABC. DE is produced to F. To prove that CF is equal and parallel to DA, we need an additional information which is
(A) ∠DAE = ∠EFC
(B) AE = EF
(C) DE = EF
(D) ∠ADE = ∠ECF

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Posted 4 months ago