NCERT Solutions for Maths Class 8 Chapter 3 Exercise 3.4 - FREE PDF Download
Class 8 Maths NCERT Solutions for Exercise 3.4, Chapter 3: Understanding Quadrilaterals provides detailed explanations for all questions in the exercise. Vedantu's subject experts created these solutions to help students successfully understand the various kinds of quadrilaterals. The main focus is on identifying the features and characteristics of different quadrilaterals, including parallelograms, trapeziums, and triangles.
This Exercise 3.4 Class 8 is important because it provides the basis for more complex geometric concepts. By studying these solutions, students can clear up their doubts and improve their knowledge of quadrilaterals. Vedantu provides clear and detailed solutions CBSE Class 8 Maths Syllabus to help students understand these concepts easily.
Glance on NCERT Solutions for Maths Chapter 3 Exercise 3.4 Class 8 | Vedantu
Exercise 3.4 Class 8 explains the main concepts of different types of quadrilaterals.
A quadrilateral is a four-sided polygon with four angles.
A parallelogram has opposite sides that are equal and parallel.
A trapezium has only one pair of parallel sides. A rhombus is a parallelogram with all sides equal.
A rectangle is a parallelogram with all angles equal to 90 degrees.
A square is a rectangle with all sides equal.
Knowing these definitions helps in recognizing and solving problems related to various quadrilaterals.
There are 6 fully solved questions in Chapter 3 Exercise 3.4 Understanding Quadrilaterals.
Exercise 3.4
1. State whether True or False.
(a) All rectangles are squares.
Ans: This statement is false.
Because all squares are rectangles but all rectangles are not square.
As in square, all sides are equal.
But in rectangles opposite sides are equal.
(b) All rhombuses are parallelograms.
Ans: This statement is true.
Because opposite sides are equal and opposite sides are parallel in a rhombus.
(c) All squares are rhombuses and also rectangles.
Ans: This statement is true.
Because in rhombuses opposite sides are equal and parallel, so as in square.
In a rectangle opposite sides are equal and parallel, so as in square.
(d) All squares are not parallelograms.
Ans: This statement is false.
All squares are parallelograms.
Because in a square all sides are equal and opposite sides are parallel.
(e) All kites are rhombuses.
Ans: This statement is false.
Because in kites opposite sides are not equal. The Diagonal top of the kite is not equal.
(f) All rhombuses are kites.
Ans:This statement is true.
As rhombuses also have two consecutive sides they are equal as in kite.
(g) All parallelograms are trapeziums.
Ans: This statement is true.
Because all parallelograms have pairs of parallel sides.
(h) All squares are trapeziums.
Ans: This statement is true.
Because all squares have a pair of parallel sides.
2. Identify all the quadrilaterals that have
(a) four sides of equal length
Ans: Square and rhombuses are the quadrilaterals which have all four sides of equal length.
(b) four right angles
Ans: Square and rectangle are the quadrilaterals which have all four angles.
3. Explain how a square is.
(i) a quadrilateral
Ans: A square is quadrilateral because it has four sides.
(ii) a parallelogram
Ans: A square is parallelogram because it’s opposite sides are of equal length and parallel. And opposite angles of the square are also equal.
(iii) a rhombus
Ans: A square rhombus is a square because the square has all sides of equal length.
(iv) a rectangle
Ans: A square is a rectangle because opposite sides are of equal length and all angles are right angles.
4. Name the quadrilaterals whose diagonals.
(i) bisect each other
Ans: Square, rectangle, rhombus and parallelogram are the quadrilaterals in which diagonals bisect each other.
(ii) are perpendicular bisectors of each other
Ans: Square and rhombus are the quadrilaterals in which diagonals are perpendicular bisectors of each other.
(iii) are equal
Ans: Rectangle, square and parallelogram are the quadrilaterals in which diagonals are equal.
5. Explain why a rectangle is a convex quadrilateral.
Ans: Rectangle is a convex quadrilateral because both diagonals of the rectangle are lying inside of the rectangle.
6. ABC is a right-angled triangle and O is the midpoint of the side opposite to the right angle. Explain why O is equidistant from A, B and C. (The dotted lines are drawn additionally to help you).
Ans:
Given :\[ABC\] is a right angle triangle in which \[\angle B\] is right angle and \[O\] is a mid-point of \[AC\] .
Construction : Draw line \[AD{\text{ and }}DC\]such that \[AD\parallel BC\]and \[AB\parallel DC\] .
And, \[AB = DC,{\text{ }}AD = BC\]
As, opposite sides are of equal length, opposite sides are parallel and also all interior angles are measure of \[90^\circ \].
Therefore, \[ABCD\] is a rectangle.
So, in a rectangle, diagonals of equal length bisect each other.
Therefore,
\[AO = OC = BO = OD\]
Hence, \[O\] is equidistant from \[A,B{\text{ and }}C\].
Conclusion
NCERT Solutions for Maths Ex 3.4 Class 8 Chapter 3 - Understanding Quadrilaterals provides simple solutions. Focus on understanding the characteristics of shapes such as squares, rectangles, parallelograms, rhombuses, and trapezoids. Understanding these features is necessary for solving problems correctly. Practising these tasks will help you develop a strong understanding of the subject and improve your geometry skills. These solutions make it easy to remember quadrilaterals and help you score well on exams.
Class 8 Maths Chapter 3: Exercises Breakdown
CBSE Class 8 Maths Chapter 3 Other Study Materials
Chapter-Specific NCERT Solutions for Class 8 Maths
Given below are the chapter-wise NCERT Solutions for Class 8 Maths. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.
Important Related Links for CBSE Class 8 Maths
FAQs on NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.4
1. What is a quadrilateral, and why is it important in geometry in Ex 3.4 Class 8?
In Ex 3.4 Class 8, a quadrilateral is a polygon with four sides and four angles. Understanding quadrilaterals is important because they form the basis for more complex shapes. They are commonly used in various real-life applications and geometry problems. Mastering quadrilaterals helps in solving Class 8 Maths Ex 3.4 advanced geometry topics.
2. What is the sum of the interior angles of a quadrilateral in Ex 3.4 Class 8?
The sum of the interior angles of any quadrilateral is always 360 degrees. This property is fundamental in geometry. It helps in solving problems related to quadrilaterals. Knowing this sum is essential for finding unknown angles, for more refer to Ex 3.4 Class 8.
3. What are the key properties of a parallelogram in Class 8 Maths Exercise 3.4?
In Class 8 Maths Exercise 3.4, a parallelogram, opposite sides are equal and parallel, and opposite angles are equal. Adjacent angles are supplementary, meaning they add up to 180 degrees. These properties are crucial for identifying and solving parallelogram problems.
4. How can you identify a rectangle among other quadrilaterals in Class 8 Maths Exercise 3.4?
A rectangle has opposite sides that are equal, and all angles are 90 degrees. Additionally, its diagonals are equal and bisect each other. These properties distinguish it from other quadrilaterals, refer to Class 8 Maths Exercise 3.4 for more solutions.
5. What makes a square different from other quadrilaterals in Class 8 Maths 3.4?
A square has all sides equal and all angles are 90 degrees. Its diagonals are equal and bisect each other at right angles. This makes it a special type of rectangle and rhombus. Refer Class 8 Maths 3.4.
6. What is the main characteristic of a rhombus in Class 8 Maths 3.4?
A rhombus has all sides equal and opposite angles equal. Its diagonals bisect each other at right angles. These properties differentiate it from other quadrilaterals in Class 8 Maths 3.4.
7. How do you define a trapezium in Class 8 Ex 3.4?
In Class 8 Ex 3.4, a trapezium is a quadrilateral with only one pair of parallel sides. This simple property makes it easy to identify. It is different from parallelograms, which have two pairs of parallel sides.
8. Why is understanding the properties of quadrilaterals important for students in Class 8 Ex 3.4?
Understanding quadrilateral properties from Class 8 Ex 3.4 helps in accurately solving geometric problems. It builds a foundation for advanced topics. This knowledge is essential for exams and real-life applications.
9. How are the diagonals of a rectangle and a square different in Class 8 Maths Ex 3.4?
According to Class 8 Maths Ex 3.4, both rectangles and squares have equal diagonals. However, in a square, the diagonals bisect each other at right angles. In a rectangle, they only bisect each other without forming right angles.
10. What should students focus on when studying Class 8 Maths Chapter 3 Exercise 3.4 Solutions?
Students should focus on understanding the properties of different quadrilaterals in Class 8 Maths Chapter 3 Exercise 3.4 Solutions. They need to practice problems related to sides, angles, and diagonals. These Solutions will help them solve questions accurately.
11. How does Exercise 3.4 help in real-life applications?
According to Class 8 Exercise 3.4, knowing quadrilateral properties is useful in fields like architecture and engineering. It helps in accurate geometric calculations. This knowledge is practical for designing and constructing various structures.
12. What are adjacent angles in a parallelogram, and why are they important in Class 8 Exercise 3.4?
In Class 8 Exercise 3.4, adjacent angles in a parallelogram share a common side. They are important because they are supplementary, adding up to 180 degrees. This property helps in solving angle-related problems.
13. How do the solutions provided by Vedantu help in understanding quadrilaterals from Class 8 Maths Chapter 3 Exercise 3.4 Solution?
Vedantu's solutions offer clear explanations for each problem in Class 8 Maths Chapter 3 Exercise 3.4 Solution. They help students understand concepts better. This builds confidence and improves problem-solving skills.
