Quadrilaterals is a core and important geometry chapter in Class 9 Mathematics that helps students understand the properties of four-sided figures. This chapter covers key concepts such as types of quadrilaterals, angle sum property, properties of parallelograms, mid-point theorem, and proofs related to diagonals and sides, which are frequently asked in school examinations.
NCERT Solutions for Class 9 Maths Chapter 8 – Quadrilaterals are prepared strictly according to the latest CBSE syllabus and exam pattern. The solutions are explained in simple, step-by-step language with clear diagrams and logical reasoning, enabling students to write accurate proofs and score well in Class 9 exams.
NCERT Solutions for Class 9 Maths Chapter 8 – Quadrilaterals
Q.
The angles of quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of the quadrilateral.
Q.
Q.
Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other.
Q.
In a parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively (see Fig. 8.31).
Show that the line segments AF and EC trisect the diagonal BD.
Q.
ABCD is a trapezium in which AB || DC, BD is a diagonal and E is the mid-point of AD.
A line is drawn through E parallel to AB intersecting BC at F (see Fig. 8.30). Show that F is the mid-point of BC.
Q.
ABCD is a rectangle and P, Q, R and S are mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.
Q.
ABCD is a rhombus and P, Q, R and S are the mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rectangle.
Q.
ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA (see the figure below). AC is a diagonal. Show that :
(i) SR||AC and SR = (1/2)AC
(ii) PQ = SR
(iii) PQRS is a parallelogram.
Q.
Q.
Q.
If the diagonals of a parallelogram are equal, then show that it is a rectangle.
Q.
Q.
ABCD is a rectangle in which diagonal AC bisects ∠A as well as ∠C. Show that:
(i) ABCD is a square.
(ii) diagonal BD bisects ∠B as well as ∠D.
Q.
ABCD is a rhombus. Show that diagonal AC bisects ∠A as well as ∠C and diagonal BD bisects ∠B as well as ∠D.
Q.
Diagonal AC of a parallelogram ABCD bisects ∠A . Show that
(i) it bisects ∠C and
(ii) ABCD is a rhombus.
Q.
Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.
Q.
Show that the diagonals of a square are equal and bisect each other at right angles.
Q.
Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.
Q.
Question
The angles of a quadrilateral are in the ratio 3 : 5 : 9 : 13.
Find all the angles of the quadrilateral.
Answer
Let the four angles of the quadrilateral be:
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First angle = 3x
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Second angle = 5x
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Third angle = 9x
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Fourth angle = 13x
According to the angle sum property of a quadrilateral, the sum of all interior angles is 360 degrees.
So,
3x + 5x + 9x + 13x = 360°
Adding the terms,
30x = 360°
Dividing both sides by 30,
x = 360° ÷ 30
x = 12°
Now, we find the value of each angle:
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First angle = 3 × 12° = 36°
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Second angle = 5 × 12° = 60°
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Third angle = 9 × 12° = 108°
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Fourth angle = 13 × 12° = 156°
Final Answer
The angles of the quadrilateral are:
36°, 60°, 108° and 156°.
FAQs: Class 9 Maths Chapter 8 – Quadrilaterals
Q1. Is Quadrilaterals an important chapter for Class 9 exams?
Yes, it is a high-weightage geometry chapter with proof-based questions.
Q2. Which topics are most important in this chapter?
Properties of parallelograms, angle sum property, and mid-point theorem.
Q3. Are proof-based questions common in this chapter?
Yes, theorem-based and reasoning questions are frequently asked.
Q4. Is this chapter useful for higher classes?
Yes, it forms the base for coordinate geometry and quadrilaterals in Class 10.
Q5. How do NCERT Solutions help?
They provide NCERT-aligned, exam-ready explanations with clear diagrams and proofs.