Question

Question 81

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

Answer 1

We draw a perpendicular to $m$ from P using

(i) set squares

Step I: let $m$ be the given line and P be a point outside $m$. Now, extend line $m$ on both the sides.

Step II: Place the set square on $m$ such that one arm of its right angle aligns along $m$.

Step III: Place a ruler along the edge opposite to the right angle of the set square.

Step IV: Hold the ruler fixed side the set square along the ruler till the point P touches the other arm of the set square.

Step V: Join PM along the edge through P meeting $m$ at O.

Now, PO $\perp$ $m$.

(ii) Protractor

Step I: let $m$ be the given line and P be a point outside $m$.

Step II: Place the protractor on point P such that its centre coincides with point P.

Step III: Mark a point B against the ${90}^0$ mark on the protractor.

Step IV: Remove the protractor and draw a line $l$ passing through P and B which intersects line $m$ at O.

Then, PO $\perp$ $m$.

(iii) Ruter and compass

Step I: Given, a line $m$ and a point P not on it. Extend the given line in both directions.

Step II: With P as centre, draw an arc which intersects line $m$ at two points A and B.

Step III: With A and B as centres and the same radius draw two arcs which intersect at a point, say Q on the other side.

Step IV: Join PQ.

Thus, PQ is perpendicular to $m$.

We can draw only one perpendicular line.