# NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry (EX 4.2) Exercise 4.2﻿

The basis of Practical Geometry is the construction of objects in diverse shapes and sizes. This is one of the most important fields of Geometry. The construction of numerous two- and three-dimensional shapes is demonstrated to students. In Practical Geometry classes, students will learn to draw these shapes accurately.

In association with Practical Geometry, students learn:

• How are parallel lines constructed? How to construct:
• A Triangle having three known sides (SSS Criterion)
• A Triangle with two given sides and a known included Angle (SAS Criterion)
• Triangle, when two angles and one included side are known (ASA Criterion)
• Right-angled Triangle with one side’s length and supplied hypotenuse (RHS Criterion)

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Geometry is a significant branch of Mathematics and an ancient branch of Science. For elementary or middle school students, it is all about different basic shapes, including their names, traits, and formulas relating to their Areas and Volumes. However, modern geometry has departed greatly from these core concepts. However, this does not imply any change in the fact that these concepts exist and the ways in which they are used in daily life. These concepts still have an effect on how people live their lives. Geometry is the most significant branch of Mathematics.

Geometry emerged as an academic field in the past, thus it has a significant impact on human life. Problems can be resolved through the application of geometrical concepts, especially in practical circumstances. Geometry has been in prevalent relevance since the days of the civilisation of ancient Egypt. They used knowledge of Geometry in many different fields, including Art, Measurement, and Building. As a consequence, beautiful temples, palaces, dams, and bridges are the remnants of Egyptian civilisation.

In addition to building and measurements, Geometry has an impact on a wide range of technical fields, such as Biological Modelling, Designing, Computer Graphics, and Typography. Students who are interested in learning more about these ancient and fascinating subject can use tools like the NCERT Solutions for Class 8 Maths Chapter 4 Exercise 4.2.

## NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry (EX 4.2) Exercise 4.2

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### Why is Geometry Important?

One of the traditional branches of Mathematics is Geometry. This concept relates to figures and space and is roughly translated from Greek into English as “Earth Measurement”. It was initially developed as a useful tool for measuring volumes, lengths, and areas, and it is still in use today. Due to the fact that the world is made up of various shapes and spaces, Geometry is significant. Numerous real-world uses for Geometry are found. Students can make use of the NCERT Solutions forClass 8 Maths Chapter 4 Exercise 4.2 to better understand this subject.

### NCERT Solutions for Class 8

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 (i) Quadrilateral LIFT (ii) Quadrilateral GOLD LI = 4 cm OL = 7.5 cm IF = 3 cm GL = 6 cm TL = 2.5 cm GD = 6 cm LF = 4.5 cm LD = 5 cm IT = 4 cm OD = 10 cm (iii) Rhombus BEND BN = 5.6 cm DE = 6.5 cm

Ans

(i) Steps of construction:

• Draw a line segment LT of length 2.5 cm.
• With L as centre, draw an arc of radius 4 cm.
• With T as centre, draw an arc of radius 4 cm intersecting the previous arc at point I.
• Join IL and IT.
• With L as centre, draw an arc of radius 4.5 cm at point F.
• With I as centre, draw an arc of radius 3 cm intersecting the previous arc at F.
• Join IF,LF and FT.

Therefore, LIFT is the required quadrilateral.

(ii) Steps of construction:

• Draw a line segment GD of length 6 cm.
• With G as centre, draw an arc of radius 6 cm.
• With D as centre, draw an arc of radius 6 cm intersecting the previous arc at point L.
• Join GL and DL.
• With D as centre, draw an arc of radius 10 cm at point O.
• With L as centre, draw an arc of radius 7.5 cm intersecting the previous arc at O.
• Join LO,DO and GO.

Therefore, GOLD is the required quadrilateral.

(iii) Steps of construction:

• Draw a line segment ED of length 6.5 cm.
• With E and D as centres draw the perpendicular bisector of ED.
• Let the lines interesect each other at O.
With O as centre, draw an arcs of radius 2.8 cm on both the sides.
• Let the arcs intersect the perpendicular bisector at B and N.
• Join NE, ND BD and BE.

Therefore, BEND is the required rhombus.