Q1.
Can you draw a line parallel to l, that goes through point A? How will you do it with the tools from your geometry box? Describe your method.
Answer
Yes. Tools needed: a ruler (scale), a set square and a pencil.
- Place one edge of the set square exactly along line l.
- Hold the ruler firmly against another edge of the set square, so the ruler cannot move — it is now a rail.
- Slide the set square along the ruler until the edge that was on l reaches point A.
- Draw a line along that edge through A.
- This new line passes through A and is parallel to l.
The set square only slides, never turns
So the drawing edge keeps the direction of l
⟹ new line ∥ l, and it passes through A
So the drawing edge keeps the direction of l
⟹ new line ∥ l, and it passes through A
Alternative method with the protractor: draw any line through A that cuts l at a point P. Measure the angle it makes with l at P. Copy that same angle at A, in the corresponding position, and draw the second arm. Equal corresponding angles make the new line parallel to l.
Alternative method with paper folding: fold a crease t through A perpendicular to l; then fold a crease m through A perpendicular to t. Then m ∥ l.
Why it happens: All three methods do the same thing in different clothing — they force the new line to make the same angle with some transversal as l does. Equal corresponding angles guarantee parallelism.
Did you know? Through a point not on a line there is exactly one line parallel to it. So whichever method you use, everyone in the class gets the same line.