## NCERT 6TH CLASS MATHEMATICS CHAPTER PRACTICAL GEOMETRY

**INTRODUCTION**

Geometric constructions are made with the aid a ruler or straightedge and compasses only. Drawings are made with the aid of additional instruments, such as protactor and ruler.

**Construction of a Circle when its Radius is Known**

Suppose you are asked to draw a circle of radius 3 cm. do as follows :

**STEP 1.**

Mark a point C with your pencil. This point will be the centre of the circle.

**STEP 2.**

Open the compass for the required radius, i.e., 3 cm, by putting the steel point on C and opening the pencil upto 3 cm.

**STEP 3.**

Hold the paper with one hand and swing the pencil leg of the compass around to draw a circle.

**Construction of a Line Segment of a Given Length :**

Suppose you have to draw a line segment 5.3 cm long.

**Method 1.**using ruler only

1. Mark any point in your exercise book and label it as A.

2. Place the ruler in such a way that the zero mark on the ruler coincides with A.

3. Now count 5 complete centimetres and 3 small divisions after the 5 cm mark and mark a point corresponding to this division on the exercise book.

4. Join A to this point as shown.

5. Label the second point as B.

Then AB is the required segment of length 5.3 cm.

**Method 2.**Using ruler and compass

**STEP 1.**

Draw any line segment which is longer than 5.3 cm.

**STEP 2.**

Mark a point on this line near one end as shown. Label it A.

**STEP 3.**

Use your compass to measure 5.3 cm on your ruler.

**STEP 4.**

Put the point of the compass on the line segment at A and draw an arc to cut the line as shown.

Then AB = 5.3 cm.

**To construct a line segment congruent to a given line segment AB**

**STEP 1.**

Draw a ray through any end point C. Open your compass so that the metal tip is on A and the pencil point is on B.

**STEP 2.**

Keep the compass opening same. Put the metal tip on the end point C of the ray and mark off a line CD congruent to AB.

Perpendicular Lines

Perpendicular lines are lines that intersect at right angles. The symbol ^ means "is perpendicular to".

Drawing Perpendicular Using Ruler and a Set- Square

**CASE 1 :** To constant a line perpendicular to a given line l at a point P lying on it.

**STEP 1. **

Place a ruler on the paper with one of its long edges lying along the line l.

**STEP 2.**

Holding the ruler fixed, place a set-square ABC with the arm AC of its right angle A in contact with the ruler.