**Practical Geometry**

**Question 1.Draw any line segment ,. Mark any point M on it. Through M, draw a perpendicular to ,. (use ruler and compasses)**

**Solution:****Steps of Construction:**

- Draw a line segment AB, and mark any point M on it.
- With centre M and any radius, cut off MX and MY of equal lengths on both sides of M.
- With centre X and any radius > MX, draw an arc.
- With centre Y and the same radius draw another arc, cutting the previously drawn arc at P
- Join MP

Then, the segment PM so obtained is the required perpendicular.

**Question 2.Draw any line segment ,. Take any point R not on it. Through R, draw a perpendicular to ,. (use ruler and set-square)**

**Solution:***Steps of Construction:*

- Let PQ be the line and R is any point not lying on PQ.
- Place the set-square so that the base AB of the set-square lies exactly on the line PQ.
- Hold the set-square fixed and place a ruler so that its edge position lies along the side AC of the set-square.
- Holding the ruler fixed, slide the set-square along the ruler till the point R coincides with the point B of the set-square.
- Keeping the set-square fixed in this position, draw a line RT along the edge BC of the set-square through R.

Thus, RT is the required perpendicular line to the line PQ passing through R.

**Question 3.**

**Draw a line l and a point X on it. Through X, draw a line segment perpendicular to l. Now draw a perpendicular to XY at Y. (use ruler and compasses)**

**Solution:***Steps of Construction:*

- Draw a line l and mark any point X on it. ,
- With centre X and any radius, cut off XA = XB on both sides of X.
- With centre A and any radius > XA, draw an arc.
- With centre B and the same radius draw another arc, cutting the previously drawn arc at Y.
- Join XY. Then XY is perpendicular to line 1.
- By proceeding as above draw a perpendicular YZ to XY.