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# NCERT Solutions for Quadrilaterals Exercise 8.2 Class 9 Maths Exercise 8.2 Class 9 Maths: The NCERT Solutions for Quadrilaterals Exercise 8.2 Class 9 Maths deals with the topic Mid-Point Theorem. In this section, students will learn about a line segment joining the mid-points of two sides of a triangle, parallel to the third side, a line drawn through the mid-point of one side of a triangle, parallel to another side bisects the third side.

Exercise 8.2 Class 9 Maths contains 7 questions. Each question is framed to help students implement the Mid-Point theorem concepts appropriately in a given question. It is important for students to solve the NCERT solutions for Quadrilaterals ex 8.2 Class 9 Maths to be able to prove the theorems in different scenarios. In this article, we have provided ex 8.2 Class 9 NCERT Solutions in pdf format for direct download. Read on to know more about the Chapter 8 Quadrilaterals.

## NCERT Solutions for Quadrilaterals Exercise 8.2 Class 9 Maths: Overview

If no three points out of four are collinear, the figure so created is a closed figure with four sides. Such a figure formed by joining four points in order is called a quadrilateral. In the ex 8.2 Class 9, students are required to prove that two sides are parallel to each other and one side is half of the other side and that the whole figure is a parallelogram.

From the given information, prove that the given figure is a rectangle, or a rhombus, from the given information, prove that a certain point is the mid-point of a side.

Before we go into the chapter summary section, check the overview of the NCERT Solutions for Quadrilaterals Exercise 8.2 Class 9 Maths Chapter 8 here:

### NCERT Solutions for Quadrilaterals Exercise 8.2 Class 9 Maths PDF

Quadrilaterals is a very extensive topic and have numerous theorems. There are also many questions that require students to prove the theorems and determine values based on relevant theorems. Students are advised to download the NCERT Solutions for Quadrilaterals exercise 8.2 Class 9 Maths in PDF format from below and solve all the questions given. The Class 9 ex 8.2 can enable students to implement the Mid-Point theorem in various conditions and arrive at a solution.

### NCERT Solutions for Quadrilaterals Exercise 8.2 Class 9 Maths: About the Exercise

In the ex 8.2 Class 9 NCERT Solutions for Quadrilaterals, there are a total of seven questions. In each question, a student has to either prove a theorem or prove any other condition based on the Mid-Point Theorem.

For example, show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other, XYZ is a triangle right angled at Z. A line through the mid-point M of hypotenuse XY and parallel to YZ intersects XZ at D. Show that (i) D is the mid-point of XZ (ii) MD ⊥ XZ (iii) ZM = MX = 1/2 of XY.

### NCERT Solutions for Quadrilaterals Exercise 8.2 Class 9 Maths: Chapter Summary

In this chapter, the following important points are explained, which are summarised below:
1. Sum of the angles of a quadrilateral is 360°.
2. A diagonal of a parallelogram divides it into two congruent triangles.
3. In a parallelogram, (i) opposite sides are equal (ii) opposite angles are equal (iii) diagonals bisect each other.
4. A quadrilateral is a parallelogram, if (i) opposite sides are equal or (ii) opposite angles are equal or (iii) diagonals bisect each other or (iv)a pair of opposite sides is equal and parallel.
5. Diagonals of a rectangle bisect each other and are equal and vice-versa.
6. Diagonals of a rhombus bisect each other at right angles and vice-versa.
7. Diagonals of a square bisect each other at right angles and are equal, and vice-versa.
8. The line segment joining the mid-points of any two sides of a triangle is parallel to the third side and is half of it.
9. A line through the mid-point of a side of a triangle parallel to another side bisects the third side.
10. The quadrilateral formed by joining the mid-points of the sides of a quadrilateral, in order, is a parallelogram.

### Benefits of Solving NCERT Solutions for Quadrilaterals Exercise 8.2 Class 9 Maths

There are many advantages of solving from Embibe NCERT Solutions exercise 8.2 Class 9 Maths, which are listed below:

1. These NCERT Solutions are prepared by Embibe’s subject experts for Class 9 Maths Chapter 8 Exercise 8.2.
2. The derivation of theorems and proving of conditions is explained step-by-step, making it easier for students to understand the theorems and solve the questions correctly.
3. Exercise 8.2 Class 9 Maths NCERT solutions are important with a view to solving tougher and more complex questions in higher classes.
4. Students can download the ex 8.2 Class 9 Maths pdf offline and practice the questions at their convenience.

### FAQs on NCERT Solutions for Quadrilaterals Exercise 8.2 Class 9 Maths

Here are some of the most frequently asked questions on NCERT Solutions for Quadrilaterals Exercise 8.2 Class 9 Maths

Q.1. Where can I get the Exercise 8.2 Class 9 Maths NCERT Solutions free PDF?

Q.2. Are NCERT Solutions Class 9 Maths sufficient for the final exam preparation?
Ans. The NCERT textbooks and Solutions are prescribed for Class 9 and are thus the only books to be referred to for CBSE Class 9 exam.

Q.3. Where can I learn the concepts of Class 9 Maths chapter 8 exercise 8.2?
Ans. Students can learn and practice the topic Mid-Point Theorem by solving the questions given in class 9 maths chapter 8 exercise 8.2.

Q.4. What are the concepts covered in the NCERT Solutions for class 9 maths chapter 8 exercise 8.2?
Ans. The NCERT Solutions Class 9 Maths Chapter 8 Quadrilateral explains theorems regarding proving a certain condition based on given information.

Q.5. How many exercises are there in Class 9 maths chapter 8 exercise 8.2?
Ans.
There are two exercises in the NCERT Solutions for Class 9 Maths chapter 8 exercise 8.2.