NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.4 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.4.

- Understanding Quadrilaterals Class 8 Ex 3.1
- Understanding Quadrilaterals Class 8 Ex 3.2
- Understanding Quadrilaterals Class 8 Ex 3.3

Board |
CBSE |

Textbook |
NCERT |

Class |
Class 8 |

Subject |
Maths |

Chapter |
Chapter 3 |

Chapter Name |
Understanding Quadrilaterals |

Exercise |
Ex 3.4 |

Number of Questions Solved |
6 |

Category |
NCERT Solutions |

## NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 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.

**Solution.**

(b), (c), (f), (g), (h) are true;

others are false.

**Question 2.**

**Identify all the quadrilaterals that have.**

**(a)** four sides of equal length

**(b)** four right angles

**Solution.**

**(a)** Rhombus; square

**(b)** Square; rectangle

**Question 3.**

**Explain how a square is**

**(i)** a quadrilateral

**(ii)**a parallelogram

**(iii)** a rhombus

**(iv)** a rectangle.

**Solution.**

**(i)** **a quadrilateral**

A square is 4 sided, so it is a quadrilateral.

**(ii)** **a parallelogram**

A square has its opposite sides parallel; so it is a parallelogram.

**(iii) a rhombus**

A square is a parallelogram with all the 4 sides equal, so it is a rhombus.

**(iv) a rectangle**

A square is a parallelogram with each angle a right angle; so it is a rectangle.

**Question 4.**

**Name the quadrilaterals whose diagonals :**

**(i)** bisect each other

**(ii)** are perpendicular bisectors of each other

**(iii)** are equal.

**Solution.**

**(i) bisect each other**

The names of the quadrilaterals whose diagonals bisect each other are parallelogram; rhombus; square; rectangle.

**(ii) are perpendicular bisectors of each other**

The names of the quadrilaterals whose diagonals are perpendicular bisectors of each other are rhombus; square.

**(iii) are equal**

The names of the quadrilaterals whose diagonals are equal are square; rectangle.

**Question 5.**

Explain why a rectangle is a convex quadrilateral.

**Solution.**

A rectangle is a convex quadrilateral because both of its diagonals lie wholly in its interior.

**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).

**Solution.**

Construction: Produce BO to D such that BO = OD. Join AD and CD.

Proof. AO = OC ∵ O is the mid-point of AC

BO = OD By construction

∴ Diagonals of quadrilateral ABCD bisect each other.

∴ Quadrilateral ABCD is a parallelogram.

Now, ∠ABC = 90° given

∴ ABCD is a rectangle.

Since the diagonals of a rectangle bisect each other, therefore,

O is the mid-point of AC and BD both. But AC = BD

∵ Diagonals of a rectangle are equal

∴ OA = OC =\(\frac { 1 }{ 2 } \)AC =\(\frac { 1 }{ 2 } \)BD = OB

⇒ OA = OB = OC.

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