Construction of Lines

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Construction of a line segment of given length

Steps to construct a line segment of length 5 cm:

Draw line l.

Mark a point on line and name it as P.

Open the compass to measure the length of the line segment by placing the pointer on the 0 mark of the ruler and the pencil point on the 5 cm mark.

Place the pointer of the compass on point P and swing an arc on the line to cut it at Q.

PQ   is the required line segment of length 5 cm.

Construction of copy of a given line segment:

Construction of a copy of line segment PQ.

  • Keep the compass pointer on P and the pencil on Q.
  • Draw line m.
  • Mark a point R on the line m.
  • Place the pointer of the compass on point R without changing its settings.
  • Swing an arc cutting line m.
  • Mark the point where the arc cuts the line, as S.
  • Line segment RS is the required copy of line segment PQ.

Two lines are said to be perpendicular when they intersect each other at an angle of 90o.

Construction of perpendicular lines

Construction of perpendicular to given line at a point on the line:

  • ‘l’ is a line and O is a point on it.
  • Draw a semi-circle with a convenient radius and 'O' as the centre.
  • Mark the points of intersection of the semi-circle and line l as P and Q.
  • Draw an arc with a radius greater than PO and P as the centre.
  • Draw another arc with the same radius and Q as the centre, so that it intersects the previous arc.
  • Mark the point of intersection of the arcs as X.
  • Join points O and X.
  • Line OX is the required perpendicular to line ‘l’.

Construction of perpendicular to given line from a point outside the line:

  • 'l’ is a line and R is a point outside the line.
  • Draw an arc with R as the centre and a convenient radius.
  • Mark the points of intersection of the arc and line l as P and Q.
  • Draw an arc on the side opposite to R with the same radius and P as the centre.
  • Draw another arc with the same radius and Q as the centre so that it intersects the previous arc.
  • Name the point of intersection of the two arcs as S.
  • Join points R and S.
  • Line RS is the required perpendicular to the given line ‘l’ passing through point R.

The perpendicular bisector is a perpendicular line that bisects another line into two equal parts.

Construction of perpendicular bisector of line segment:

  • Draw a line segment and name it as PQ.
  • Open the compass for a radius more than half the length of PQ.
  • Draw a circle with P as the centre.
  • Draw another circle with the same radius and the centre as Q .
  • Name the points of intersection of the two circles as R and S.
  • Join points R and S.
  • Name the point at which RS intersects PQ as M .
  • RS is the perpendicular bisector of PQ.

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