Class 8 Exam  >  Class 8 Notes  >  NCERT Solutions (Ex - 3.4) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8

NCERT Solutions (Ex - 3.4) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 PDF Download

Exercise 3.4

Question 1: 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.

Answer 1:

(a) False. Since, squares have all sides are equal.

(b) True. Since, in rhombus, opposite angles are equal and diagonals intersect at mid-point.

(c) True. Since, squares have the same property of rhombus but not a rectangle.

(d) False. Since, all squares have the same property of parallelogram.

(e) False. Since, all kites do not have equal sides.

(f) True. Since, all rhombuses have equal sides and diagonals bisect each other.

(g) True. Since, trapezium has only two parallel sides.

(h) True. Since, all squares have also two parallel lines.

Question 2:

Identify all the quadrilaterals that have:

(a) four sides of equal lengths.

(b) four right angles.

Answer 2:

(a) Rhombus and square have sides of equal length.

(b) Square and rectangle have four right angles.

Question 3:

Explain how a square is:

(i) a quadrilateral

(ii) a parallelogram

(iii) a rhombus

(iv) a rectangle

Answer 3:

(i) A square is a quadrilateral, if it has four unequal lengths of sides.

(ii) A square is a parallelogram, since it contains both pairs of opposite sides equal.

(iii) A square is already a rhombus. Since, it has four equal sides and diagonals bisect at 90o to each other.

(iv) A square is a parallelogram, since having each adjacent angle a right angle and opposite sides are equal.

Question 4:

Name the quadrilateral whose diagonals:

(i) bisect each other.

(ii) are perpendicular bisectors of each other.

(iii) are equal.

Answer 4:

(i) If diagonals of a quadrilateral bisect each other then it is a rhombus, parallelogram, rectangle or square.

(ii) If diagonals of a quadrilateral are perpendicular bisector of each other, then it is a rhombus or square.

(iii) If diagonals are equal, then it is a square or rectangle.

Question 5:

Explain why a rectangle is a convex quadrilateral.

Answer 5:

A rectangle is a convex quadrilateral since its vertex are raised and both of its diagonals lie in its interior. (www.tiwariacademy.com) (Class – VIII) A Free web support in Education 3

Question 6:

ABC is a right-angled triangle and O is the mid-point 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.)

Answer 6:

Since, two right triangles make a rectangle where O is equidistant point from A, B, C and D because O is the mid-point of the two diagonals of a rectangle.

Since AC and BD are equal diagonals and intersect at mid-point.

So, O is the equidistant from A, B, C and D.

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FAQs on NCERT Solutions (Ex - 3.4) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8

1. What is the importance of understanding quadrilaterals in mathematics?
Ans. Understanding quadrilaterals is important in mathematics because they are the building blocks for more complex shapes and figures. They help in the study of geometry, measurement, and various mathematical concepts. Quadrilaterals also have real-life applications in fields such as architecture, engineering, and design.
2. How many types of quadrilaterals are there?
Ans. There are several types of quadrilaterals, including parallelograms, rectangles, squares, rhombuses, trapeziums, and kites. Each type has its own unique properties and characteristics.
3. What are the properties of a square?
Ans. A square is a type of quadrilateral with four equal sides and four right angles. Its properties include: - All sides are equal in length. - All angles are right angles (90 degrees). - Diagonals are equal in length and bisect each other at right angles. - Opposite sides are parallel and congruent.
4. How can one determine if a quadrilateral is a parallelogram?
Ans. A quadrilateral can be determined as a parallelogram if it satisfies the following conditions: - Opposite sides are parallel. - Opposite sides are congruent. - Opposite angles are congruent. - Diagonals bisect each other.
5. What is the difference between a rectangle and a rhombus?
Ans. The main difference between a rectangle and a rhombus lies in their angles. A rectangle has four right angles (90 degrees) while a rhombus has four equal angles that are not necessarily right angles. Additionally, a rectangle has opposite sides that are parallel and congruent, while a rhombus has opposite sides that are parallel but not necessarily congruent.
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