# 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.

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.

### 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. ### STEP 3.

Slides the set-sq