Question

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 perpendicular are you able to draw?

Answer 1

We draw 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, extended line m on both the sides.

Step II: Place a 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 tight angle of the set square.

Step IV: Hold the ruler fixed. Slide 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 ⊥ m.

(ii) Protractor

Step I: Let m be the given line and P be a point putside m.

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

Step III: Mark a point B againt the 90° 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 ⊥ m.

(iii) Ruler 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 entre, 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 are able to draw one perpendicular line.