# Bisecting a Line Segment

In this section we will discuss bisecting a line segment.Bisect means divide the line segment in two equal parts.

**Bisecting a Line Segment**

Draw a line segment measuring 5 cm and its perpendicular bisector. Write the steps of construction.

Step 1 : Draw a line segment AB of length 5 cm.

Step 2 : Mark two arcs with radius more than half of AB with centers A and B respectively.

Step 3 : These arcs intersect at P and Q respectively.

Step 4 : Join P and Q.

Step 5 : PQ is required perpendicular bisector of line segment AB.

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**Construction of a line perpendicular to a given line at a given point using Ruler and Compass**

Draw any line segment AB . Mark any point P on it. Through P, draw a perpendicular to segment AB with the help of ruler and compasses.

Step 1: Given a point P on a line l.

Step 2: With P as center and a convenient radius, construct an arc intersecting the line l at two points A and B.

Step 3: With A and B as centers and a radius greater than AP construct two arcs, which cut each other at Q.

Step 4: Join PQ.

Thus PQ is perpendicular to l.

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**Construction of a line perpendicular to a given line and passing through a given point not lying on it by using ruler and compasses.**

Draw any line segment AB . Take any point P outside it. Through P, draw a perpendicular to segment AB.

Step 1: Given a line l and a point P outside it.

Step 2: With P as center, draw an arc, which intersects line l at two points A and B.

Step 3: Using the same radius and with A and B as centers, construct two arcs that intersect at a point, say Q, on the other side.

Step 4: Join PQ.

Thus, segment PQ is perpendicular to line l.

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**Geometrical Constructions**

• Basic Geometric Constructions

• Construction of Line Segment

• Bisecting a Line Segment

• Constructing Angles

• Bisecting Angles

• Constructing Parallel Lines

• Construction of Triangle (SSS)

• SAS Triangle Construction

• ASA Triangle Construction

• HL Triangle Construction (Rhs -construction)

• Constructing Quadrilaterals

• Constructing Triangles(when sum of sides or perimeter is given)

• Basic Geometric Constructions

• Construction of Line Segment

• Bisecting a Line Segment

• Constructing Angles

• Bisecting Angles

• Constructing Parallel Lines

• Construction of Triangle (SSS)

• SAS Triangle Construction

• ASA Triangle Construction

• HL Triangle Construction (Rhs -construction)

• Constructing Quadrilaterals

• Constructing Triangles(when sum of sides or perimeter is given)