Question

5. In the given figure, BE and CF are two
equal altitudes of ∆ABC.
Show that (i) ∆ABE =~ ∆ACF,
(ii) AB = AC.​

Answer 1

Step-by-step explanation:

In ΔABE and ΔACF,

∠BAE=∠CAF (Common angle)

∠AEB=∠AFC ....(∵BE⊥AC and CF⊥AB)

BE=CF (Given that altitudes are equal)

By AAS criterion of congruence,

ΔABE≅ΔACF

Hence,

AB=AC (by CPCT)

Answer 2

Answer:

In ∆ABC and ∆ACE, we have

BE=CF-(Given)

∆BEA=∆CFA=90°

∆A=∆A-(Common)

∆ABE=~∆ACF

(ii) AB=AC (C.P.C.T)