**Introduction:**

The word “geometry” is derived from the combination of two Greek words “geo” and “metron”. The word “Geo” means “earth” and “metron” means “measurement”. geometry have the both practical and theoretical applications.Knowledge of geometry is helpful in every walk of our dailylife. While Constructing roads we draw its map and ensure its route with the help of geometry only.

## Constructions with ruler and Compasses - geometry construction act:

**Bi-section of a Line Segment - geometry construction act:**

Find a point M on a given line segment AB which divides AB in two equal parts so that AM = BM

** Steps of construction - geometry construction act:**

1. With centre A of the line segment AB and radius a little more than half the length of the line segment, draw an arc of a circle on both thesides of the line segment.

2.Now with B,the other point of line segment as centre and same radius draw another two arcs on both the sides of AB,which will intersect the former arcs,respectively at E and F.

3.Join points E and F with the help of scale,intersecting line segment AB at M.

BI-SECTION OF LINE SEGMENT

## Construction of a Perpendicular on any Point of the Given line - geometry construction act:

Construction of a Perpendicular on any Point of the Given line Given a line segment XY.

P is any point on it. It is required to draw a line passing through P, which is perpendicular to XY

**Steps of Construction :**

(1) Draw an arc of circle with any radius from P, as centre, which intersects line XY at A and B

(2) With centre A, draw another arc of a circle, with radius more than half P A.

(3) With B as centre and same radius as above draw another arc of the circle which intersects the first arc at Q

(4) Join points P and Q and find line segment PQ. It can be produced too, in both ways. measure angle QPB, verify QPB = 90°

Thus PQ is perpendicular to the line segment XY.