Class 9 Exam > Class 9 Notes > Mathematics (Maths) Class 9 > Unit Test: Quadrilaterals
Unit Test: Quadrilaterals | Mathematics (Maths) Class 9 PDF Download
Time: 1 hour
M.M. 30
Attempt all questions.
Question numbers 1 to 5 carry 1 mark each.
Question numbers 6 to 8 carry 2 marks each.
Question numbers 9 to 11 carry 3 marks each.
Question numbers 12 & 13 carry 5 marks each.
Q1. Which of the following is not a quadrilateral? (1 Mark)
(a) Kite
(b) Square
(c) Triangle
(d) Rhombus
Q2. The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rectangle, if (1 Mark)
(a) PQRS is a rectangle
(b) PQRS is a parallelogram
(c) Diagonals of PQRS are perpendicular
(d) Diagonals of PQRS are equal
Q3. Three angles of a quadrilateral are 75º, 90º and 75º. The fourth angle is (1 Mark)
(a) 90º
(b) 95º
(c) 105º
(d) 120º
Q4. Which of the following is not true for a parallelogram? (1 Mark)
(a) Opposite sides are equal
(b) Opposite angles are equal
(c) Opposite angles are bisected by the diagonals
(d) Diagonals bisect each other.
Q5. A trapezium has: (1 Mark)
(a) One pair of opposite sides is parallel
(b) Two pairs of opposite sides parallel to each other
(c) All its sides are equal
(d) All angles are equal
Q6. In a parallelogram, one angle measures 60°. Find the measures of all other angles. (2 Marks)
Q7. Find the perimeter of the quadrilateral with sides 5 cm, 7 cm, 9 cm and 11 cm. (2 Marks)
Q8. Determine the area of a parallelogram with a base of 5 cm and a height of 3 cm. (2 Marks)
Q9. The perimeter of the quadrilateral is 50 cm and the lengths of the three sides are 9 cm, 13 cm and 17 cm. Find the missing side of the quadrilateral. (3 Marks)
Q10. In a rectangle, one diagonal is inclined to one of its sides at 25°. Measure the acute angle between the two diagonals. (3 Marks)
Q11. Calculate all the angles of a quadrilateral if they are in the ratio 2 : 5 : 4 : 1. (3 Marks)
Q12. In an isosceles trapezium ABCD, AB ∥ CD and AD = BC. Show that ∠A = ∠B and ∠C = ∠D. (5 Marks)
Q13. Show that the diagonals of a rhombus bisect each other at right angles. (5 Marks)
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FAQs on Unit Test: Quadrilaterals - Mathematics (Maths) Class 9
| 1. What are quadrilaterals and what are their main properties? |  |
Ans. Quadrilaterals are four-sided polygons. The main properties of quadrilaterals include having four edges and four vertices. The sum of the interior angles of any quadrilateral is always 360 degrees. Quadrilaterals can be classified into various types such as squares, rectangles, parallelograms, trapeziums, and rhombuses, each having its unique properties related to sides, angles, and symmetry.
| 2. How can you classify quadrilaterals based on their sides and angles? | |
Ans. Quadrilaterals can be classified based on their sides and angles into several categories:
1. Parallelogram: Opposite sides are equal and parallel.
2. Rectangle: All angles are right angles, and opposite sides are equal.
3. Square: All sides are equal, and all angles are right angles.
4. Rhombus: All sides are equal, but angles are not necessarily right angles.
5. Trapezium: Only one pair of opposite sides is parallel.
These classifications help in understanding their properties and solving related problems.
| 3. What is the difference between a convex and a concave quadrilateral? | |
Ans. A convex quadrilateral is one where all interior angles are less than 180 degrees, and no vertices point inwards. In contrast, a concave quadrilateral has at least one interior angle greater than 180 degrees, which causes one or more vertices to point inwards. This distinction is important in geometric studies as it affects the properties and calculations related to the shape.
| 4. Can you explain the concept of the diagonals of a quadrilateral? | |
Ans. The diagonals of a quadrilateral are the line segments that connect opposite vertices. A quadrilateral can have two diagonals. The properties of the diagonals vary based on the type of quadrilateral: in a parallelogram, the diagonals bisect each other; in a rectangle, they are equal in length; and in a rhombus, they bisect each other at right angles. Understanding the diagonals is essential for solving many geometric problems.
| 5. How is the area of different types of quadrilaterals calculated? | |
Ans. The area of quadrilaterals can be calculated using different formulas depending on their type:
1. Rectangle: Area = length × width.
2. Square: Area = side × side.
3. Parallelogram: Area = base × height.
4. Trapezium: Area = ½ × (sum of parallel sides) × height.
5. Rhombus: Area = ½ × (diagonal₁ × diagonal₂).
These formulas allow for the calculation of area based on known dimensions and are fundamental in geometry.
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