Practical Geometry Class 7 Notes: Chapter 10

Lines That Don’t Meet

Method of construction of a line parallel to a given line, using only a sheet of paper

1. Take a piece of paper.
2. Fold it in half and unfold the line $l$. Mark a point A on paper outside $l$.
3. Fold the paper perpendicular to the line such that this perpendicular passes through A. Name the perpendicular AN.
4. Make a fold perpendicular to AN through point A. Name the new perpendicular line as $m$.
5. Now,  $l$ || $m$.

Steps of construction of a line parallel to a given line

1. Take a line $l$ and a point A outside $l$.
2. Take any point B on $l$ and join it to A.
   
3. With B as the centre and a convenient radius, cut an arc on $l$ at C and BA at D.
   
4. With A as the centre and same radius as in Step 3, cut an arc EF to cut AB at G.
   
5. Measure the arc length CD by placing pointed tip of the compass at C and pencil tip opening at D.
6. With this opening, keep G as centre and draw an arc to cut arc EF at H
   
7. Join AH to draw a line $m$
   

∠ABC and ∠BAH are alternate interior angles. Therefore, $m$ || $l$