Important Questions Class 9 Maths Chapter 8 Quadrilaterals are provided here that cover different question variations which will help the students to get thoroughly acquainted with all the concepts. These CBSE class 9 questions for quadrilaterals include several short answers, long answer and HOTS type questions which will let the students develop their problem-solving skills.
These CBSE Class 9 Maths Chapter 8 Important Questions on Quadrilateral help students to prepare most effectively for the final exams and face it most confidently. Solving these important questions is the best practise for students
Important Questions Class 9 Maths Chapter 8 Quadrilaterals with Solutions
Go through the following important questions for class 9 Maths Chapter 8 Quadrilateral to understand the concepts quickly and it helps to solve the problems having similar patterns.
1. What is a quadrilateral? Mention 6 types of quadrilaterals.
Solution:
A quadrilateral is a 4 sided polygon having a closed shape. It is a 2-dimensional shape.
The 6 types of quadrilaterals include:
- Rectangle
- Square
- Parallelogram
- Rhombus
- Trapezium
- Kite
2. The diagonals of which quadrilateral are equal and bisect each other at 90°?
Solution:
Square. The diagonals of a square are equal and bisect each other at 90°.
3. Identify the type of quadrilaterals:
(i) The quadrilateral formed by joining the midpoints of consecutive sides of a quadrilateral whose diagonals are perpendicular.
(ii) The quadrilateral formed by joining the midpoints of consecutive sides of a quadrilateral whose diagonals are congruent.
Solution:
(i) The quadrilateral formed by joining the midpoints of consecutive sides of a quadrilateral whose diagonals are perpendicular is a rectangle.
(ii) The quadrilateral formed by joining the midpoints of consecutive sides of a quadrilateral whose diagonals are congruent is a rhombus.
4. Find all the angles of a parallelogram if one angle is 80°.
Solution:
For a parallelogram ABCD, opposite angles are equal.
So, the angles opposite to the given 80° angle will also be 80°.
It is also known that the sum of angles of any quadrilateral = 360°.
So, if ∠A = ∠C = 80° then,
∠A + ∠B + ∠C + ∠D = 360°
Also, ∠B = ∠D
Thus,
80° + ∠B + 80° + ∠D = 360°
Or, ∠B +∠ D = 200°
Hence, ∠B = ∠D = 100°
Now, all angles of the quadrilateral are found which are:
∠A = 80°
∠B = 100°
∠C = 80°
∠D = 100°
5. In a rectangle, one diagonal is inclined to one of its sides at 25°. Measure the acute angle between the two diagonals.
Solution:
Let ABCD be a rectangle where AC and BD are the two diagonals which are intersecting at point O.
Now, assume ∠BDC = 25° (given)
Now, ∠BDA = 90° – 25° = 65°
Also, ∠DAC = ∠BDA, (as diagonals of a rectangle divide the rectangle into two congruent right triangles)
So, ∠BOA = the acute angle between the two diagonals = 180° – 65° – 65° = 50°
6. Is it possible to draw a quadrilateral whose all angles are obtuse angles?
Solution:
It is known that the sum of angles of a quadrilateral is always 360°. To have all angles as obtuse, the angles of the quadrilateral will be greater than 360°. So, it is not possible to draw a quadrilateral whose all angles are obtuse angles.
7. Prove that the angle bisectors of a parallelogram form a rectangle.
Solution:
LMNO is a parallelogram in which bisectors of the angles L, M, N, and O intersect at P, Q, R and S to form the quadrilateral PQRS.
LM || NO (opposite sides of parallelogram LMNO)
L + M = 180 (sum of consecutive interior angles is 180o)
MLS + LMS = 90
In LMS, MLS + LMS + LSM = 180
90 + LSM = 180
LSM = 90
RSP = 90 (vertically opposite angles)
SRQ = 90, RQP = 90 and SPQ = 90
Therefore, PQRS is a rectangle.
8. In a trapezium ABCD, AB∥CD. Calculate ∠C and ∠D if ∠A = 55° and ∠B = 70°
Solution:
In a trapezium ABCD, ∠A + ∠D = 180° and ∠B + ∠C = 180°
So, 55° + ∠D = 180°
Or, ∠D = 125°
Similarly,
70° + ∠C = 180°
Or, ∠C = 110°
9. Calculate all the angles of a parallelogram if one of its angles is twice its adjacent angle.
Solution:
Let the angle of the parallelogram given in the question statement be “x”.
Now, its adjacent angle will be 2x.
It is known that the opposite angles of a parallelogram are equal.
So, all the angles of a parallelogram will be x, 2x, x, and 2x
As the sum of interior angles of a parallelogram = 360°,
x + 2x + x + 2x = 360°
Or, x = 60°
Thus, all the angles will be 60°, 120°, 60°, and 120°.
10. Calculate all the angles of a quadrilateral if they are in the ratio 2:5:4:1.
Solution:
As the angles are in the ratio 2:5:4:1, they can be written as-
2x, 5x, 4x, and x
Now, as the sum of the angles of a quadrilateral is 360°,
2x + 5x + 4x + x = 360°
Or, x = 30°
Now, all the angles will be,
2x =2 × 30° = 60°
5x = 5 × 30° = 150°
4x = 4 × 30° = 120°, and
x = 30°
Important Question Class 9 Maths Chapter 8 Quadrilaterals for Practice
Solve the following important questions for class 9 Maths chapter 8 quadrilaterals to score good marks.
- The angles of a quadrilateral are in the ratio of 3: 5: 9: 13. Determine all the angles of a quadrilateral.
- A quadrilateral is a _____, if its opposite sides are equal. (a) Trapezium (b) Kite (c) Parallelogram (d) Cyclic quadrilateral.
- If one angle of a parallelogram is 30° less than twice the smallest angle, then determine the measurement of each angle.
- Prove that the diagonal of a parallelogram divides it into two congruent triangles.
- ABCD is a rhombus with ∠ABC = 50°. Determine ∠ACD.
- ABC is a triangle. D, E, and F are the midpoints of AB, BC and CA respectively. Show that by joining these midpoints D, E and F, a triangle ABC is divided into four congruent triangles.
- ABCD is a rhombus with ∠ABC = 40°. The measure of ∠ACD is ____. (a) 20° (b) 40° (c) 70° (d) 90°
- ABCD is a quadrilateral in which P, Q, R, S are the midpoints of the sides AB, BC, CD and DA respectively. AC is the diagonal. Prove that: (a) PQRS is a parallelogram (b) PQ = SR (c) SR || AC and SR = ½ AC.
- Show that the diagonals of a rectangle are equal in length.
- Prove that the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.