In Fig. 6.40, E is a point on side CBproduced of an isosceles triangle ABCwith AB = AC. If AD ⊥ BC and EF ⊥ AC,prove that Δ ABD ~ Δ ECF

Question

In Fig. 6.40, E is a point on side CBproduced of an isosceles triangle ABCwith AB = AC. If AD &#x22A5; BC and EF &#x22A5; AC,prove that &#x394; ABD ~ &#x394; ECF

Philoid · Accepted Answer

Given that ABC is an isosceles triangle

AB = AC

⇒∠ABD = ∠ECF

In ΔABD and ΔECF,

∠ADB = ∠EFC (Each 90°)

∠BAD = ∠CEF (Proved above)

ΔABD ΔECF (By using AA similarity criterion)