Question

Copy figure on your notebook and draw a perpendicular to l through P, using (i) set squares (ii) protractor (iii) ruler and compass. How many such perpendiculars are you able to draw?

Answer 1

We draw perpendicular to l through P, using

(i) Set square

Steps of construction are as follows:

Step I: A line l and a point P are given. Note that P is on the line l.

Step II: Place a ruler with one of its edges along l. Hold it firmly.

Step III: Place a set square with one of its edges along the already aligned edge of the ruler, such that the right angled corner is in contant with the ruler.

Step IV: Slide the set square along the edge of ruler unit its right angled corner concides with P.

Step V: Hold the set square along the edge of ruler unit its right angled corner coincides with P.

(ii) Protractor

Step I: A line l and a point P are given. Note that P is on the line l.

Step II: Place the protractor on the line, such that its base line coincides with l and its centre falls on P.

Step III: Mark a point B against the 90° mark on the protractor.

Step IV: Remove the protractor and draw a line m passing through P and B.

Then, PB ⊥ l.

(iii) Ruler and Compass

Step I: Given, a point P on a line l.

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

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

Step IV: Join PQ. Then, PQ is perpendicular to l.

Hence, we are able to draw one perpendicular line.