Question
Copy Figure on your notebook and draw a perpendicular to l through $P,$ using $(i)$ set squares $(ii)$ Protractor $(iii)$ ruler and compasses. How many such perpendiculars are you able to draw?
✓
Answer
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 comer is in contact with the ruler.
Step $IV:$ Hold the set square firmly in this position. Draw $\overline{\text{PQ}}$ along the edge of the set square.
$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 $90^\circ$ mark on the protractor.
Step $IV:$ Remove the protractor and draw a line m passing through $P$ and $B.$
Then, $\text{PB}\bot\text{l}$
$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 redius 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.
$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 comer is in contact with the ruler.
Step $IV:$ Hold the set square firmly in this position. Draw $\overline{\text{PQ}}$ along the edge of the set square.
$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 $90^\circ$ mark on the protractor.
Step $IV:$ Remove the protractor and draw a line m passing through $P$ and $B.$
Then, $\text{PB}\bot\text{l}$
$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 redius 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.
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