If, l, m, n are three lines such that l || m and n ⊥ l , prove that n ⊥ m .

Question

If, l, m, n are three lines such that l || m and n &#x22A5; l , prove that n &#x22A5; m .

Philoid · Accepted Answer

Given that,

l ‖ m and n perpendicular to m

Since, l ‖ m and n intersects them at G and H respectively

Therefore,

∠1 = ∠2 (Corresponding angles)

But, ∠1 = 90^o as n is perpendicular to l

Therefore, ∠2 = 90^o

Hence, n is perpendicular to m.