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NCERT Solutions Ganita Prakash (Part 1) Chapter 5 Activity 3 — Corresponding Angles

Book page 116 Updated on2026-09-05

Q1.
Activity 3: Draw a pair of lines and a transversal such that they form two distinct angles. Step 1: Draw a line l and a transversal t intersecting it at point X. Step 2: Measure ∠a formed by lines l and t (let us say it is 60°). Step 3: Mark a point Y on line t. Step 4: Draw a line m through point Y that forms a 60° angle to line t.
Answer

Follow the four steps with a ruler and a protractor.

  1. Draw line l, then draw t cutting it at X.
  2. Measure ∠a between l and t. Suppose it comes to 60°.
  3. Mark any point Y further along t.
  4. At Y, set off 60° from t — on the same side and in the same position as ∠a — and draw line m.
∠a = 60° (at X, between l and t)
∠b = 60° (at Y, between m and t)
∠a and ∠b are corresponding angles
Only two sizes appear anywhere: 60° and 120°
Why it happens: Copying the angle at Y makes line m lean exactly like line l. Every angle at Y is then a copy of the matching angle at X, so no new sizes can appear.
Tip: Instead of a protractor you may trace ∠a on tracing paper and slide the tracing along t up to Y. Copying is more accurate than measuring.
Q2.
How many distinct angles have formed now?
Answer

Only two distinct angles: 60° and 120°.

At X: ∠a = 60°
Linear pair → 180° – 60° = 120°
Vertically opposite → 60° and 120° again
At Y the same two values repeat
Total distinct measures = 2
Why it happens: One angle fixes all four at a crossing — the angle itself, its supplement, and their two facing copies. Since we deliberately copied 60° at Y, the second crossing repeats the very same two values.
Q3.
What do you observe about lines l and m? Do they appear to be parallel to each other?
Answer

Yes, l and m appear to be parallel — and they really are.

Corresponding angles ∠a = ∠b = 60°
Equal corresponding angles ⟹ l ∥ m
Why it happens: The angle a line makes with the transversal tells you how much that line leans. Since l and m make the same 60° with t, they lean by the same amount, so the gap between them never changes and they can never meet.
Did you know? This is the important rule of the chapter: when the corresponding angles made by a transversal on a pair of lines are equal, the lines are parallel. It is a way of testing for parallelism without extending the lines at all.
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