Q1:
Draw a line and name it PQ, take a point R outside it. Through R, draw a line parallel to PQ using the ruler and compass only.
Solution:
To construct: A line, parallel to the given line by using ruler and compass.
Construction:
(i) Draw a line segment PQ and take a point R outside PQ.
(ii) Take any point X on PQ and join R to X.
(iii) With X as the center and take convenient radius, draw an arc cutting PQ at Y and RX at Z.
(iv) With R as center and the same radius as in step (iii), draw an arc AB cutting PX at O
(v) With the same arc YZ, draw the equal arc cutting AB at M.
(vi) Join MR to draw a line N.
This the required line PQ ǁ N
Q2 :
Draw a line N. Draw a perpendicular to N at any point on N. On this perpendicular choose a point P, 4cm away from N. Through A, draw a line P parallel to N.
Solution:
To construct: A line parallel to given line when perpendicular line is also given.
Construction:
(i) Draw a line N and take a point O on it.
(ii) At point O, draw a perpendicular line Q
(iii) Take OA = 4 cm on line Q.
(iv) At point A again draw a perpendicular line P
It is the required construction.
Q3:
Let X be a line and A be a point not on X. Through A, draw a line Y parallel to X. Now join A to any point B on X. Choose any point C on Y. Through C, draw a line parallel to AB. Let this meet X at P. What shape do the two sets of parallel lines enclose?
Solution:
To construct: A pair of parallel lines intersecting other part of parallel lines.
Construction:
(i) Draw a line X and take a point A outside of X
(ii) Take point B on line X and join AB
(iii) Make equal angle at point A such that Ð B = Ð A
(iv) Extend line at A to get line Y
(v) Similarly, take a point C which intersects at P on line X, draw line PC
Thus, we get parallelogram ABCP
