In each of the following, draw perpendicular through point P to the line segment AB :
In each of the following, draw perpendicular through point P to the line segment AB :
(i) Steps of Construction :
1. With P as centre, draw an arc of a suitable radius which cuts AB at points C and D.
2. With C and D as centres, draw arcs of equal radii and let these arcs intersect each other at the point Q.
[The radius of these arcs must be more than half of CD and both the arcs must be drawn on the other side]
3. Join P and Q
4. Let PQ cut AB at the point O.
Thus, OP is the required perpendicular clearly, ∠AOP=∠BOP=90∘
(ii) Steps of Construction :
1. With P as centre, draw an arc of any suitable radius which cuts A B at points C and D.
2. With C and D as centres, draw arcs of equal radii. Which intersect each other at the point A.
[This radius must be more than half of CD and let these arc]
[This radius must be more than half of CD and let these arc intersect each other at the point O]
3. Join P and O. Then OP is the required perpendicular.
∴ ∠OPA=∠OPB=90∘
(iii) Steps of Construction :
1. With P as centre, draw an arc of any suitable radius which cuts AB at points C and D.
2. With C and D as centre, draw arcs of equal radii [The radius of these arcs must be more than half of CD and both the arcs must be drawn on the other side.]
and let this arcs intersect each other at the point Q.
3. Join Q and P. Let QP cut AB at the point O. Then OP is the required perpendicular.
Clearly, ∠AOP=∠BOP=90∘
(i) Steps of Construction :
1. With P as centre, draw an arc of a suitable radius which cuts AB at points C and D.
2. With C and D as centres, draw arcs of equal radii and let these arcs intersect each other at the point Q.
[The radius of these arcs must be more than half of CD and both the arcs must be drawn on the other side]
3. Join P and Q
4. Let PQ cut AB at the point O.
Thus, OP is the required perpendicular clearly, ∠AOP=∠BOP=90∘
(ii) Steps of Construction :
1. With P as centre, draw an arc of any suitable radius which cuts A B at points C and D.
2. With C and D as centres, draw arcs of equal radii. Which intersect each other at the point A.
[This radius must be more than half of CD and let these arc]
[This radius must be more than half of CD and let these arc intersect each other at the point O]
3. Join P and O. Then OP is the required perpendicular.
∴ ∠OPA=∠OPB=90∘
(iii) Steps of Construction :
1. With P as centre, draw an arc of any suitable radius which cuts AB at points C and D.
2. With C and D as centre, draw arcs of equal radii [The radius of these arcs must be more than half of CD and both the arcs must be drawn on the other side.]
and let this arcs intersect each other at the point Q.
3. Join Q and P. Let QP cut AB at the point O. Then OP is the required perpendicular.
Clearly, ∠AOP=∠BOP=90∘
