NCERT Solutions Ganita Prakash (Part 1) Chapter 5 In-text Questions — Alternate Angles

Book page 120 Updated on2026-09-05

Q1.
Why are lines l and m parallel to each other? (Making Parallel Lines through Paper Folding, Fig. 5.24)
Answer

Because both of them are perpendicular to the same crease t.

Fold 1: crease t ⟂ l, passing through A
Fold 2: crease m ⟂ t, passing through A
Treat t as a transversal of l and m
Corresponding angles = 90° and 90° → equal
l ∥ m
Why it happens: A fold that lays a line exactly on top of itself must be perpendicular to that line. So each fold creates a true right angle — no measuring needed. Two lines that make the same 90° with a common transversal lean the same way, hence they are parallel.
Tip: This is the folding version of the set-square method on page 118. Both rest on the same rule: two lines perpendicular to one line are parallel to each other.
Q2.
Activity 6: In Fig. 5.25, if ∠f is 120° what is the measure of its alternate angle ∠d?
Answer

∠d = 120°.

∠f = 120° (given)
∠b = ∠f = 120° (corresponding angles, l ∥ m)
∠d = ∠b = 120° (vertically opposite angles)
So ∠d = 120°

The same chain works for any value of ∠f:

∠f = ∠b (corresponding)
∠b = ∠d (vertically opposite)
Therefore ∠f = ∠d, always
Why it happens: To find the alternate angle of ∠f, first step across to its corresponding angle ∠b at the other line, then turn to the facing angle ∠d. Each step preserves the size, so the two ends of the chain must be equal — without any measurement.
Did you know? This proves the rule: alternate angles formed by a transversal intersecting a pair of parallel lines are always equal. In Fig. 5.25, ∠c and ∠e are the other alternate pair.
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