# Practical Geometry

## Exercise 10.1

Question 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. Answer: Draw a line AB and then plot a point C which is outside the line AB.
From the point A, draw another line which passes through C.
With A as centre, draw a semi-circle on AB.
With C as centre, draw a semi-circle on the line which passes through C.
With the same radius as in above circles, and point Q as centre draw an arc which intersects the semi-circle drawn above.
Draw the line MN which is parallel to AB.

Question 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. Make a 90° angle at one end of this line.
Draw a line to show a perpendicular line.
Plot a point X which is at a distance of 4 cm from point P.
Taking X as centre, draw a perpendicular on this vertical line.
Draw XU which is perpendicular to line l.

Question 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 D on m. Through D, draw a line parallel to PQ. Let this meet l at S. What shape do the two sets of parallel lines enclose? Answer: Draw a line L and plot a point P which is not on this line.
Join one end of the line to point P.
With one end of line L as centre, draw an arc.
With P as centre (same radius as above), draw an arc; as shown.
With B as centre, draw an arc which intersects the previous arc.
Draw a line PM which is parallel to line L.
Take any point Q on line L and join this with point P.
Follow above steps to draw a line parallel to PQ from point D on line PM.
The resulting figure is a parallelogram.