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Question -

ABC is an isosceles triangle in which AB = AC. BE and CF are its two medians. Show that BE = CF.



Answer -

Given : In ∆ABC, AB = AC
BE and CF are two medians
 
To prove : BE = CF
Proof: In ∆ABE and ∆ACF.
AB = AC (Given)
∠A = ∠A (Common)
AE = AF (Half of equal sides)
∴ ∆ABE ≅ ∆ACF (SAS axiom)
∴ BE = CF (c.p.c.t.)

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