CBSE Class 7 Mathematics: Practical Geometry NCERT Solutions

To construct a line parallel to a given line AB through an external point C using ruler and compasses, follow these steps:

1. Draw a line segment AB and mark a point C that is not on AB.
2. Choose any point D on the line AB and draw a line segment connecting C to D. This segment acts as a transversal.
3. Place the compass point on D and draw an arc that intersects AB at a point E and the segment CD at a point F.
4. Without changing the compass radius, place the compass point on C and draw an arc (let's call it GH) that intersects the segment CD at a point I.
5. Adjust the compass to the length EF (the distance between E and F). Place the compass point on I and draw an arc that intersects the arc GH at a point J.
6. Join the points C and J with a straight line. Extend this line to form line l.

The line l drawn through C is parallel to the line AB.

To construct a line m parallel to a given line l, using a perpendicular line:

1. Draw a line l and select any point P on it.
2. Construct a line n perpendicular to line l at point P.
3. Measure 4 cm along the perpendicular line n starting from P and mark this point as X. So, $PX\; =\; 4$ cm.
4. At point X, construct a line m perpendicular to the line n.

The line m is the required line parallel to line l, and it is 4 cm away from l.

To construct the shape enclosed by two sets of parallel lines:

1. Draw a line l and choose a point P that is not on l.
2. Select a point Q on line l and draw the line segment PQ.
3. Construct a line m passing through P such that m is parallel to l. This can be done using methods from Question 1 or 2.
4. Choose a point R on the newly constructed line m.
5. Now, draw a line through R that is parallel to the line segment PQ. Let this line intersect line l at a point S.

The shape enclosed by the two pairs of parallel lines (line m parallel to l, and line RS parallel to PQ) is a parallelogram. The vertices of this parallelogram are P, Q, S, and R, forming PQSR.