NCERT Solutions Class 8 Maths Chapter 3 Understanding Quadrilaterals Exercise 3.4

The NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.4 explains the mid-point theorem and its application to solve geometry problems especially triangles and quadrilaterals. The exercise contains both reasoning-type questions and calculation-type questions. NCERT Solutions of this exercise will help you understand how connecting mid-points of a triangle will change the shape and sides. These kinds of questions come up quite often in school tests and CBSE exams, therefore making its learning essential.

These solutions provided in a step by step manner are based on the latest NCERT syllabus for Class 8 and are useful to develop logical thinking and problem-solving skills, which is important for school exams and other competitive exams like the Olympiads. Whether you are learning for class assessments or just want a better understanding of the topic, this PDF will help you learn with confidence.

1.0Download NCERT Solutions Class 8 Maths Chapter 3 Understanding Quadrilaterals Exercise 3.4: Free PDF

Exercise 3.4 of The NCERT Solutions Class 8 Maths Chapter 3 is related to the midpoint theorem and its application in triangles. The questions are solved step by step to help the learning of the concept. Download the free PDF of the solutions from below:

2.0Key Concepts in Exercise 3.4 of Class 8 Maths Chapter 3

This task will primarily focus on the mid-point theorem and how to use it in questions relating to geometry. You will learn the following concepts:

• Mid-point theorem and its statement
• Application of mid-point theorem in triangles
• Using geometrical figures to prove relationships
• Simple reasoning to solve problems based on shapes.

3.0NCERT Class 8 Maths Chapter 3: Other Exercises

4.0NCERT Class 8 Maths Chapter 3 Exercise 3.4: Detailed Solutions

• State whether True or False : (a) All rectangles are squares. (b) All rhombuses are parallelograms. (c) All squares are rhombuses and also rectangles. (d) All squares are not parallelograms. (e) All kites are rhombuses. (f) All rhombuses are kites. (g) All parallelograms are trapeziums. (h) All squares are trapeziums. Sol. (a) False (b)True (c) True (d) False (e) False (f) True (g) True (h) True
• Identify all the quadrilaterals that have : (a) Four sides of equal length. (b) Four right angles. Sol. (a) The quadrilaterals having four sides of equal length is either a square or a rhombus. (b) The quadrilaterals having four right angles is either a square or a rectangle.
• Explain how a square is (i) A quadrilateral (ii) A parallelogram (iii) A rhombus (iv) A rectangle Sol. (i) A square is 4 sided, so it is a quadrilateral. (ii) A square has its opposite sides parallel, so it is a parallelogram. (iii) A square is a parallelogram with all the four sides equal, so it is a rhombus. (iv) A square is a parallelogram with each angle a right angle, so it is a rectangle.
• Name the quadrilaterals whose diagonals : (i) bisect each other. (ii) are perpendicular bisectors of each other. (iii) are equal. Sol. (i) The quadrilaterals whose diagonals bisect each other can be a parallelogram or a rhombus or a square or a rectangle. (ii) The quadrilaterals whose diagonals are perpendicular bisectors of each other can be a rhombus or a square. (iii) The quadrilaterals whose diagonals are equal can be a square or a rectangle.
• Explain why a rectangle is a convex quadrilateral. Sol. Since the measure of each angle is less than $180^{\circ }$ and also both the diagonals of a rectangle lie wholly in its interior, so a rectangle is a convex quadrilateral.
• ABC is a right angled triangle and $O$ is the mid point of the side opposite to the right angle. Explain why 0 is equidistant from A, B and C. Sol.
  
  Produce BO to D such that BO = OD. Join $AD$ and $DC$. Then $ABCD$ is a rectangle. In the rectangle $ABCD$, its diagonals $AC$ and $BD$ are equal and bisect each other at 0 , $\therefore \mathrm{OA}=\mathrm{OC}$ and $\mathrm{OB}=0\mathrm{D}$. But AC = BD Therefore, $\mathrm{OA}=\mathrm{OB}=\mathrm{OC}$ Thus, O is equidistant from $\mathrm{A},\mathrm{B}$ and C . The mid point of diagonal $\overline{\mathrm{AC}}$ is 0 .

5.0Key Features and Benefits of Class 8 Maths Chapter 3 Exercise 3.4

• The chapter follows the midpoint theorem as per the updated NCERT syllabus.
• Enhance visual understanding of geometry using diagram-based questions.
• The NCERT Solutions are written in simple steps for clear understanding.
• Practice of these solutions enhances logical thinking and problem solving skills which can be useful while participating in Math Olympiad.