question_answer 13)

Draw any line segment \[{{l}_{1}},{{l}_{2}}\] Mark any point M on it. Through M, draw a perpendicular to \[{{l}_{3}}\](use ruler and compasses).

Answer:

                To draw a perpendicular to \[{{l}_{1}},{{l}_{2}},{{l}_{3}}\] we use the following steps: Step I Firstly, draw a line segment \[\overline{AB}\] and take any point M on it. Step II With M as centre and a convenient radius, construct an arc intersecting the line \[{{l}_{4}}\] at two points X and Y. Step III With X and Y as centres and a radius greater than \[{{l}_{1}}\] construct two arcs which cut each other at D. Step IV Now, join MD. Then, \[{{l}_{2}}\] is perpendicular to \[{{l}_{1}}\] and we can write it as \[{{l}_{1}}\]