**Practical Geometry**

**Exercise 10.1**

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.

Step 1: Draw a line AB

Step 2: Take any point C outside the line AB.

Step 3: Take any point D on line AB other than A and B

Step 4: Join points C and D.

Step 5: With D as a centre and with a convenient radius draw arc that cuts

AB at M and CD at N.

Step 6: Now with C as a centre and same radius as in Step 5 draw an arc XY

Step 7: Place the pointed tip of the compasses at M and adjust the opening

So that the pencil tip is at N.

Step 8: With the same opening as in step 7 and with C as a centre, draw an

arc cutting the arc PQ at P.

Step 9: Join the points C and P.

CP is the required parallel line.

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*.

Step 1: Draw a line *l*.

Step 2: Take any point A on the line *l* and from this point draw a perpendi-

lar line with the help of a protractor (or using a set square).

Step 3: With the help of a compass measure 4 cm on the ruler.

Step 4: Put the tip of the compass on the point A and cut the perpendicular

With the help of the compass. Mark this point as X.

Step 5: Now with A as a centre and with a convenient radius draw an arc

cutting line *l* at point C and the perpendicular at D.

Step 6: Now with the X as the centre and the same radius as in the step 6

draw an arc MN

Step 7: Place the pointed tip of the compasses at C and adjust the opening

So that the pencil tip is at D.

Step 8: With the same opening as in step 7 and with X as a centre, draw an

arc cutting the arc MN at Y.

Step 9: Join the points X and Y.

XY is the required parallel line.

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?

Step 1: Draw a line *l*.

Step 2: Take any point Q on the line and a point P outside the line *l* and

from this point draw a line segment PQ

Step 3: Now with Q as a centre and with a convenient radius draw an arc

cutting line *l* at point C and the PQ at D.

Step 4: Now with the P as the centre and the same radius as in the step 3

draw an arc XY

Step 5: Place the pointed tip of the compasses at C and adjust the opening

So that the pencil tip is at D.

Step 6: With the same opening as in step 5 and with P as a centre, draw an

arc cutting the arc XY at M.

Step 7: Join the points P and M. This is the line *m* parallel to line *l*.

Step 8: Take a point R outside the line *m*. draw seg PR.

Step 9: Now with P as a centre and with a convenient radius draw an arc ST

cutting line *m* at point S and the PR at T.

Step 10: Now with the R as the centre and the same radius as in the step 9

draw an arc AB

Step 11: Place the pointed tip of the compasses at S and adjust the opening

So that the pencil tip is at T.

Step 12: With the same opening as in step 11 and with R as a centre, draw

an arc cutting the arc AB at W.

Step 13: Join the points R and W. RW is parallel to line m.

Step 14: Take any point S on the line l and join R and S passing through W.

The shape formed is parallelogram.

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