Drawing a Perpendicular to a Line

In geometry, drawing perpendicular lines is a fundamental skill. Whether constructing geometric shapes, designing buildings, or solving problems, knowing how to draw a perpendicular from a point outside or on a line is essential. 

1. Draw a line on paper and name it MN.
2. Mark a point P outside the line MN.

3. Fold the paper along line MN (just to keep it in view; don’t crease yet).

4. Now, fold the paper again, this time making sure:

• Point P touches the line MN.
• One side of the line overlaps exactly with the other.
  

5. Unfold the paper. The fold you just created intersects line MN at a specific point. Name this point Q.
6. Draw a line PQ along the fold.

7. Use a protractor to measure the angles at point Q.
Each angle measures 90°.
Therefore, line PQ is perpendicular to line MN.
Therefore: PQ ⊥ MN

1. Draw a line and name it RS.
2. Mark a point M anywhere on line RS.
3. Place the protractor so that:

• The protractor's centre point is located at M.
• The baseline of the protractor matches line RS.

4. Find the 90° mark on the protractor and mark a point N at that position.
5. Draw a line through points M and N.
6. This new line MN is perpendicular to line RS at point M. (Line MN ⊥ line RS).

1. Draw a line and name it PQ.

2. Mark a point R anywhere on line PQ.
3. Place the set square so that:

• The right-angle corner of the set square is exactly at point R.
• Line PQ is where one arm of the right angle is situated.

4. Draw a line RS along the other arm of the set square.
5. Now, line RS is perpendicular to line PQ at point R.

1. Create a straight line and give it the name XY.

2. Mark a point P, anywhere outside the line XY.

3. Place one arm of the right angle of the set square along line XY.

4. Slide the set square along line XY until the other arm of the right angle passes through point P.

5. Draw a line along that side of the set square, which touches point P.
Name this line, PS.

6. Use a protractor to measure the angle at the point of intersection.
The angle will measure 90°, confirming that line PS is perpendicular to line XY.

1. Draw a line and name it MN.
2. Mark a point K anywhere on the line MN.
3. Position the compass at point K.

• Draw two arcs on either side of K to cut line MN.
• Name the intersection points A and B (both at an equal distance from K).

4. Now, place the compass at point A :

• With a distance greater than half AB, draw an arc above or below the line.
  

5. Next, position the compass at point B.

• Using the same compass width, draw another arc to intersect the first one.
• Name the point of intersection T.

6. Draw a line passing through points K and T.
7. Now, line KT is perpendicular to line MN at point K.
Therefore: KT ⊥ MN

1. Create a line and label it MN.

2. Mark a point K outside the line MN.

3. Place the compass at point K and:

• Draw an arc that cuts the line MN at two points.
• Name those points A and B.
  

4. Place the compass at point A:

• Take a distance more than half of AB.
• Draw an arc below the line MN.

5. Place the compass at point B:

• Using the same compass width, draw another arc to intersect the previous arc.
• Mark the point of intersection as T.
  

6. Create a straight line connecting point K to point T.

7. Line KT is perpendicular to line MN.
8. You can verify by measuring the angle at the intersection — it should be 90°.

• The fundamental goal of these constructions is to create a perfect 90° angle.

• You can construct perpendiculars using:

  • Paper folding

  • Set squares

  • Compass and ruler