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NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals Ex 8.2

NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals Ex 8.2 are prepared by askIITians Maths experts to help you understand the exercise thoroughly. There are 2 exercises in this chapter that are focused on different types of quadrilaterals, properties of a parallelogram, how we can call a quadrilateral a parallelogram and the mid-point theorem and its converse. You can download the NCERT solutions for free from askIITians website and prepare this exercise easily. 

About NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals Ex 8.2

Exercise 8.2 of NCERT Grade 9 Maths Chapter 8 Quadrilaterals is based on the mid-point theorem and its converse. According to the mid-point theorem the line segment joining the mid-points of two sides of a triangle is parallel to the third side. According to the converse of the mid-point theorem, the line drawn through the midpoint of one side of a triangle, parallel to another side bisects the third side.

Other important points about quadrilaterals that you must know are:

  • There are different types of quadrilaterals like trapezium, square, rectangle, parallelogram, rhombus, and kite. 
  • A square is a rectangle and also a rhombus. 
  • A parallelogram is a trapezium. 
  • A kite is not a parallelogram. 
  • A trapezium is not a parallelogram (as only one pair of opposite sides is parallel in a trapezium and we require both pairs to be parallel in a parallelogram).  
  • A rectangle or a rhombus is not a square.
  • If in a quadrilateral, each pair of opposite angles is equal, then it is a parallelogram. 
  • Angle-Sum Property of a Quadrilateral: The sum of the angles of a quadrilateral is 360º.

Download NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals Ex 8.2

NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals Ex 8.2 include 7 questions. You can download the PDF solutions for this exercise for free from our website. Let us see what is included in each question of this exercise. 

Ex 8.2 Q1: In the first question, you are given a quadrilateral and you have to prove the given statements based on the mid-point theorem. Our NCERT solutions include a proper explanation for this question. 

Ex 8.2 Q2: In this question, you are given a rhombus along with the mid-points. You have to show that it is a rectangle. You can easily solve this question if you understand the mid-point theorem. 

Ex 8.2 Q3: This question is quite opposite of the second question. Here you are given a rectangle and its midpoints and you have to prove that it is a rhombus. 

Ex 8.3 Q4: In this question, you are given a trapezium and you have to find the midpoint of one of its sides. You must draw the diagram given in the question to understand what all information is given to you so that you can solve the question easily. 

Ex 8.2 Q5: In this question, you are given a parallelogram with the midpoints of its two sides. You have to prove that the line segments joining the mid-points trisect the diagonal of the parallelogram. 

Ex 8.2 Q6: In this question, you have to show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other.

Ex 8.2 Q7: In this question, you have to apply the midpoint theorem on a right-angled triangle and prove the statements given to you. Simply download our NCERT solutions for grade 9 Maths Chapter 8 Exercise 8.2 and get clarity on how to solve this question. 

A few tips on how to solve the NCERT questions of Class 9 Maths Chapter 8 Ex 8.2: 

  • Always draw the diagram based on the question to understand what information you have and what you need to do. 
  • Memorise the important definitions and results so that you can apply them without thinking much. 
  • Practice all NCERT problems as your final exam will be based on that only. 

Important Features of NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals Ex 8.2

  • The NCERT Solutions for quadrilaterals are prepared by experienced and qualified askIITians faculty. 
  • Every solution is explained in a stepwise format for clarity and conceptual understanding. 
  • The NCERT Class 9 Maths solutions are available for free to all students. 
  • One does not need any further guidance in understanding the solutions, they are self-explanatory. 
  • All the solutions for Class 9 Maths Chapter 8 Ex 8.2 are based on the latest CBSE exam pattern and syllabus. 

NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals Ex 8.2 FAQs

  1. I need additional help in preparing the quadrilaterals chapter. What should I do? 

askIITians provides a plethora of study materials for quadrilaterals including revision notes, worksheets, mind maps, flashcards and extra questions. You can enrol in our live classes and study all concepts from our experts. 

  1. What is the midpoint theorem?

The midpoint theorem states that the line segment joining the midpoints of any two sides of a triangle is parallel to the third side and equal to half of the third side. 

  1. Name 6 special quadrilaterals. 

The 6 special quadrilaterals are parallelogram, rectangle, rhombus, square, trapezium and kite.


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