Question

In the given figure, BE and CF are two equal altitudes of △ ABC. Show that

(i) △ ABE ≅ △ ACF,

(ii) AB = AC.

Answer 1

(i) Based on the △ ABE and △ ACF

We know that

∠ AEB = ∠ AFC = 90^o

It is given that BE = CF

From the figure we know that ∠ A is common for both ∠ BAE and ∠ CAF

So we get

∠ BAE = ∠ CAF = ∠ A

Therefore, by ASA congruence criterion we get

△ ABE ≅ △ ACF

(ii) As we know that △ ABE ≅ △ ACF

It is proved that AB = AC.