In Figure $ \mathrm{BA}\left|\right|\mathrm{ED} \mathrm{and} \mathrm{BC}\left|\right|\mathrm{EF}. $Show that $ \angle \mathrm{ABC}=\angle \mathrm{DEF}$ [Hint: Produce $ \mathrm{DE}$ to intersect $ \mathrm{BC}$ at $ \mathrm{P}$ (say)].
Prove the required statement:
Given: BA||EDandBC||EF.
Construction: Extend DE to P
∠DEF=∠DPC-(1) (corresponding angles)
∠ABC=∠DPC-(2) (corresponding angles)
From (1) and (2)
∠ABC=∠DEF
Hence proved ∠ABC=∠DEF.
Prove that the curves x = y2 and xy = k cut at right angles if 8k2 = 1. [Hint: Two curves intersect at right angle if the tangents to the curves at the point of intersection are perpendicular to each other.]
