NCERT Solutions Class 8th Maths Chapter – 3 Understanding Quadrilaterals Exercise – 3.4

NCERT Solutions Class 8th Maths Chapter - 3 Understanding Quadrilaterals Exercise 3.4
Last Doubt

NCERT Solutions Class 8th Maths Chapter – 3 Understanding Quadrilaterals

TextbookNCERT
Class8th
SubjectMathematics
Chapter3rd
Chapter NameUnderstanding Quadrilaterals
CategoryClass 8th Maths
Medium English
SourceLast Doubt

NCERT Solutions Class 8th Maths Chapter – 3 Understanding Quadrilaterals Exercise 3.4 In this chapter we will read about Understanding Quadrilaterals, What are the basics of understanding quadrilaterals?, What is an example of understanding a quadrilateral?, What is understanding quadrilaterals class 8 introduction in english?, What is a quadrilateral Class 8 maths understanding?, What are the 4 properties of a quadrilateral?, What is quadrilateral formula and solve Class 8th Maths Chapter – 3 Understanding Quadrilaterals Exercise 3.4

NCERT Solutions Class 8th Maths Chapter – 3 Understanding Quadrilaterals

Chapter – 3

Understanding Quadrilaterals

Exercise – 3.4

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.

Solution:

(a) False. Because, all square are rectangles but all rectangles are not square.

(b) True

(c) True

(d) False. Because, all squares are parallelograms as opposite sides are parallel and opposite angles are equal.

(e) False. Because, for example, a length of the sides of a kite are not of same length.

(f) True

(g) True

(h) True

2. Identify all the quadrilaterals that have.

(a) four sides of equal length
(b) four right angles

Solution:

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

(b) Square and rectangle have four right angles.

3. Explain how a square is.

(i) a quadrilateral
(ii) a parallelogram
(iii) a rhombus
(iv) a rectangle 

Solution:

(i) Square is a quadrilateral because it has four sides.

(ii) Square is a parallelogram because it’s opposite sides are parallel and opposite angles are equal.

(iii) Square is a rhombus because all the four sides are of equal length and diagonals bisect at right angles.

(iv)Square is a rectangle because each interior angle, of the square, is 90°

4. Name the quadrilaterals whose diagonals.

(i) bisect each other
(ii) are perpendicular bisectors of each other
(iii) are equal 

Solution:

(i) Parallelogram, Rhombus, Square and Rectangle

(ii) Rhombus and Square

(iii)Rectangle and Square

5. Explain why a rectangle is a convex quadrilateral.

Solution:

Rectangle is a convex quadrilateral because both of its diagonals lie inside the rectangle.

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).

Solution:

AD and DC are drawn so that AD || BC and AB || DC
AD = BC and AB = DC
ABCD is a rectangle as opposite sides are equal and parallel to each other and all the interior angles are of 90°.
In a rectangle, diagonals are of equal length and also bisects each other.
Hence, AO = OC = BO = OD
Thus, O is equidistant from A, B and C.

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