Drawing Parallel Lines

Class 7 Maths · Chapter 5: Parallel and Intersecting Lines · NCERT Ganita Prakash section 5.7

Learn

With a ruler and a set square: draw line l. Slide the set square along l and draw two lines along its right-angle edge. Both make 90° with l. Seeing l as a transversal, the corresponding angles are equal (90° and 90°), so the two new lines are parallel.

Through a given point A: put one edge of the set square on l, hold a ruler against another edge, then slide the set square along the ruler until its edge reaches A, and draw. The edge keeps the same angle with the ruler all along, so the corresponding angles stay equal.

By paper folding: for a crease l and a point A, fold a crease t through A perpendicular to l. Then fold a crease m through A perpendicular to t. Both l and m make 90° with t: equal corresponding angles, so l ∥ m.

l ⊥ t and m ⊥ t → l ∥ m

Drawing parallel lines by eye works for flat, upright or 45° lines on dot paper, but slanted lines are tricky. Instead of trusting the eye, Neel checks with angles: if a transversal makes equal corresponding angles, the lines really are parallel.

Explore: steps with a set square.

1. Put the steps for drawing a parallel line through A in order.

Remember

• A set square slid along a ruler draws parallel lines: the corresponding angles stay equal.
• Two lines perpendicular to the same line are parallel.

Quick check

Two lines both make 90° with line t. What can you say about them?

1. they are parallel
2. they are perpendicular to each other
3. they meet on t
4. nothing

Think about it

Why are two creases folded perpendicular to the same crease t parallel?

Practice

Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.