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
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.