Transversals and Corresponding Angles

Class 7 Maths · Chapter 5: Parallel and Intersecting Lines · NCERT Ganita Prakash section 5.5–5.6

Learn

A line t that crosses two lines l and m is a transversal. It makes 8 angles, numbered 1 to 8 here: 1, 2, 3, 4 where it crosses l and 5, 6, 7, 8 where it crosses m. Vertically opposite angles are equal (∠1 = ∠3, ∠2 = ∠4 …), so there are at most 4 different sizes.

Angles in the same position at the two crossings are corresponding angles: ∠1 and ∠5, ∠2 and ∠6, ∠3 and ∠7, ∠4 and ∠8. Ishaan draws line l, a transversal at 60°, and through another point on t a line m that also makes 60°. Lines l and m come out parallel!

Both ways: if the corresponding angles are equal, the lines are parallel. And if the lines are parallel, the corresponding angles are equal (trace one on tracing paper: it fits exactly on the other). If l and m are not parallel, corresponding angles can never be equal.

∠2 = ∠6 ⇔ l ∥ m

So with parallel lines, only two sizes are left. If ∠2 = 65°: ∠4, ∠6, ∠8 are 65° too, and ∠1, ∠3, ∠5, ∠7 are 180° − 65° = 115°. Corresponding angles give us a test for parallel lines that does not need extending them forever.

Explore: turn line m.

1. Turn line m until it is parallel to l.
2. Now make ∠6 = 75°. Are the lines parallel?

Remember

• A transversal makes 8 angles; corresponding angles sit in the same position at each crossing.
• Corresponding angles are equal exactly when the lines are parallel.

Quick check

l ∥ m and ∠3 = 110°. What is ∠7?

1. 110°
2. 70°
3. 180°
4. 55°

Think about it

Can 5 of the 8 angles made by a transversal all have different sizes?

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.