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

**Ex 3.4 Class 8 Maths 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.**

**(a)** False

**(b)** True

**(c)** True

**(d)** False

**(e)** False

**(f)** True

**(g)** True

**(h)** True

**Ex 3.4 Class 8 Maths Question 2.**

**Identify all the quadrilaterals that have.**

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

**(b)** four right angles

**Solution.**

**(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.

**Ex 3.4 Class 8 Maths Question 3.**

**Explain how a square is**

**(i)** a quadrilateral

**(ii)**a parallelogram

**(iii)** a rhombus

**(iv)** a rectangle.

**Solution.**

**(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.

**Ex 3.4 Class 8 Maths Question 4.**

**Name the quadrilaterals whose diagonals :**

**(i)** bisect each other

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

**(iii)** are equal.

**Solution.**

**(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.

**Ex 3.4 Class 8 Maths Question 5.**

Explain why a rectangle is a convex quadrilateral.

**Solution.**

Since the measure of each angle is less than 180° and also both the diagonals of a rectangle he wholly in its interior, so a rectangle is a convex quadrilateral.

**Ex 3.4 Class 8 Maths 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.

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 O.

∴ OA = OC and OB = OD.

But AC = BD

Therefore, OA = OB = OD

Thus, O is equidistant from A, B and C.

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