Question
Copy Figure on your notebook and draw a perpendicular from $P$ to line m, using $(i)$ set squares $(ii)$ Protractor $(iii)$ ruler and compasses. How many such perpendiculars are you able to draw?
✓
Answer
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, extend 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 right 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, $\text{PO}\bot\text{m.}$
$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 $90^\circ$ mark on the protractor.
Step $IV:$ Remove the protractor and draw a line $l$ passing through $P$ and $B$ wich intersects line m at $O.$
Then, $\text{PO}\bot\text{m}.$
$iii.\ $Ruler and Compass:
Step $I:$ Given, a line m and point $P,$ not it. Extend the given line in both derections.
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 redius 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.
$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 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 right 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, $\text{PO}\bot\text{m.}$
$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 $90^\circ$ mark on the protractor.
Step $IV:$ Remove the protractor and draw a line $l$ passing through $P$ and $B$ wich intersects line m at $O.$
Then, $\text{PO}\bot\text{m}.$
$iii.\ $Ruler and Compass:
Step $I:$ Given, a line m and point $P,$ not it. Extend the given line in both derections.
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 redius 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.
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