Question

In the given figure, AB = AC and E is a point on CB produced. If AD is perpendicular to BC and EF perpendicular to AC, prove that ΔABD is similar to ΔCEF.

Answer 1

In ΔABD and ΔCEF
AB = AC (Given)

∠ABC = ∠ACB (Equal sides have equal opposite angles)

⇒ ∠ABD = ∠ECF
∠ADB = ∠EFC   (Each 90°)
So, ΔABD ~ ΔECF   (AA - Similarity)