Ncert exemplar solutions mathematics class 9 Solutions for Chapter 5 introduction to euclids geometry

Exercises in Chapter 5 introduction to euclids geometry Grade 9

Introduction to Euclid's Geometry – Exercise 5.1

Introduction to Euclid's Geometry – Exercise 5.2

Introduction to Euclid's Geometry – Exercise 5.3

Introduction to Euclid's Geometry – Exercise 5.4

Questions in Introduction to Euclid's Geometry – Exercise 5.1

The three steps from solids to points are:

(A) Solids – surfaces – lines – points

(B) Solids – lines – surfaces – points

(D) Lines – surfaces – points – solids

The number of dimensions, a solid has:

(A) 1

(B) 2

(D) 0

The number of dimensions, a surface has:

(A) 1

(B) 2

(D) 0

The number of dimension, a point has:

(A) 0

(B) 1

(D) 3

Euclid divided his famous treatise “The Elements” into:

(A) 13 chapters

(B) 12 chapters

(D) 9 chapters

The total number of propositions in the Elements are:

(A) 465

(B) 460

(D) 55

Boundaries of solids are:

(A) Surfaces

(B) Curves

(D) Points

Boundaries of surfaces are:

(A) Surfaces

(B) Curves

(D) Points

In Indus Valley Civilisation (about 3000 B.C.), the bricks used for construction work were having dimensions in the ratio

(A) 1 : 3 : 4

(B) 4 : 2 : 1

(D) 4 : 3 : 2

A pyramid is a solid figure, the base of which is

(A) Only a triangle

(B) Only a square

(D) Any polygon

The side faces of a pyramid are:

(A) Triangles

(B) Squares

(D) Trapeziums

Questions in Introduction to Euclid's Geometry – Exercise 5.2

Euclidean geometry is valid only for curved surfaces.

The edges of a surface are curves.

The boundaries of the solids are curves.

It is known that x + y = 10 and that x = z. Show that z + y = 10?

The things which are double of the same thing are equal to one another.

Questions in Introduction to Euclid's Geometry – Exercise 5.3

Two salesmen make equal sales during the month of August. In September, each salesman doubles his sale of the month of August. Compare their sales in September.

Look at the Fig. . Show that length AH > sum of lengths of AB + BC + CD.

In the Fig. , we have AB = BC, BX = BY. Show that AX = CY.

In the Fig. , we have X and Y are the mid-points of AC and BC and AX = CY. Show that AC = BC.

In the Fig , we have BX = ½ AB, BY = ½ BC and AB = BC. Show that BX = BY.

Questions in Introduction to Euclid's Geometry – Exercise 5.4

Read the following statement:

An equilateral triangle is a polygon made up of three line segments out of which two line segments are equal to the third one and all its angles are 60° each. Define the terms used in this definition which you feel necessary. Are there any undefined terms in this? Can you justify that all sides and all angles are equal in an equilateral triangle?

Study the following statement:

“Two intersecting lines cannot be perpendicular to the same line”.

Check whether it is an equivalent version to the Euclid’s fifth postulate.