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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