# NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.4

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.4 (Ex. 14.4) Practical Geometry updated for academic session 2021-2022 free to use online or download. All the contents are in PDF and Videos format free to use without any registration on the website.

In class 6 math exercise 14.4 questions are based on the concept to drawing perpendicular on a given line. Here we will learn how to plot a perpendicular line to a given line at specific point.## Class 6 Maths Chapter 14 Exercise 14.4 Solution

### CBSE NCERT Class 6 Maths Chapter 14 Exercise 14.4 Solution in Hindi and English Medium

Class: 6 | Mathematics |

Chapter: 14 | Practical Geometry |

Exercise: 14.4 | NCERT Book’s Solutions |

### Class 6 Maths Chapter 14 Exercise 14.4 Solution in Videos

#### Construction Using Ruler and Compasses

##### Bisection of a Line Segment

Bisection of a line segment XY means dividing it into two equal parts or finding a point O on XY, such that XO = OY.

One way of bisecting a line segment is to measure it and mark off a point exactly half the length from one end of the line segment. But, this method of bisecting line segment is not accurate because the divisions on a ruler are limited.

Therefore, an accurate measurement of the line segment is not possible.

###### To bisect a given line segment using a ruler and compasses only, we take the following steps:

Step-1: Draw a line segment XY of given length.

Step-2: With X as centre and radius more than half of XY, draw arcs, one each side of XY.

Step-3: With Y as centre and the same radius as before, draw arcs, cutting the previously drawn arcs at M and N respectively.

Step-4: Join MN intersecting XY at O. Then, O bisects the line segment XY.

Verification: Measure XO and OY, you will find that XO = OY.

Important Note: The line MN divides the line segment XY into two equal parts. If you measure angle MOY, you will find that it is a right angle. So, MN Ʇ XY. For this reason, MN is called the perpendicular bisector of XY. Thus, if you are required to draw the perpendicular bisector of XY, the steps of constructions would be the same as above.

##### To Draw an Angle of Given Measure

In order to construct an angle of a given measure say, 130°, we take the following steps:

Step-1: Draw a ray, say LK with the end point L on a sheet of paper.

Step-2: Place the protractor in such a way that its centre point lies on L and its base line lies along LK.

Step-3: Run your eyes along the scale whose 180° mark lies on LK until you find 130° mark on the rim.

Step-4: On that mark put a dot with a fine pencil and name it M.

Step-5: Remove the protractor and draw a ray LM.

### Class 6 Maths Exercise 14.4 Important Questions

##### How do you construct a 600 angle?

Constructing a 60° angle

(i) open the compass to the same dimensions as our original line.

(ii) place the point of the compass on one end of the line and draw an arc.

(iii) repeat this at the other end and the arcs should intersect where the tip of the triangle should be.

##### How are angles used in construction?

Its purpose in architecture is to assure symmetry and balance when designing the look of the structure. Vertical Angles are angles opposite each other when two lines or segments cross each other. In Architecture, it is used to ensure that window panes, windows, and doors are proportionate and even.

##### What is Angle construction?

“Construction” in Geometry means to draw shapes, angles or lines accurately. These constructions use only compass, straightedge (i.e. ruler) and a pencil. This is the “pure” form of geometric construction: no numbers involved.