1. Draw a line, say AB, take a point C outside it. Through C, draw a line parallel to AB using ruler and compasses only.

Solution:

Steps for construction,

Step 1. Draw a line AB.

Step 2. Take any point L on AB and a point S outside AB and join LS.

Step 3. With L as center draw an arc to cut AB at P.

Step 4. With S as the center and same radius draw an arc HG.

Step 5. Place the pointed tip of the compass at P and adjust the opening so that the pencil tip is at F.

Step 6. With the same opening as in step 5 and with G as the center, draw an arc cutting the arc at H.

Step 7. Now, join SH to draw a line CD.

Figure:

2. Draw a line L. Draw a perpendicular to L at any point on L. On this perpendicular choose a point X, 4 cm away from l. Through X, draw a line m parallel to L.

Solution:

Steps for construction,

Step 1. Draw a line L.

Step 2. Take any point P on line L.

Step 3. At point P, draw a perpendicular line N.

Step 4. Place the pointed tip of the compass at P and adjust the compass up to the length of 4 cm, draw an arc to cut this perpendicular at point X.

Step 5. At point X, again draw a perpendicular line M.

Figure:

3. Let L be a line and P be a point not on L. Through P, draw a line m parallel to L. Now join P to any point Q on L. Choose any other point R on m. Through R, draw a line parallel to PQ. Let this meet L at S. What shape do the two sets of parallel lines enclose?

Solution:

Steps for construction,

Step 1. Draw a line L.

Step 2. Take any point Q on L and a point P outside L and join PQ.

Step 3. The angles at point P and point Q are must be equal i.e. ∠Q = ∠P

Step 4. At the point, P extends the line to get line M which is parallel to line L.

Step 5. Then take any point R on line M.

Step 6. At point R draw angle such that ∠P = ∠R

Step 7. At the point, R extends the line which intersects line L at S and draw a line RS.

Figure: