Question

prove that BE =CF

pls pls
​

Answer 1

Step-by-step explanation:

it is easiest method, i hope this will help you

please mark me as brainliest it's a humble request.

In the Δs ABE, ACF

AB=AC given

AE=AF half of AC, AB resp.

∠BAE=∠CAF common

Therefore ΔABE≅ΔACF two sides and included angle

since both triangles are congruent, then there all sides will be of same length

In particular, BE=CF

You don't need to prove FE∥BC, nor to quote the base angles of an isoceles triangle theorem.

In fact the same proof applies whenever points E and F are equidistant from A on the sides AC,AB (not necessarily the mid points). This is used in Euclid's proof of Proposition 5 (the base angles of an isoceles triangle theorem), though he could, more elegantly, have used the fact that ΔABC≅ΔACB (two sides and the included angle).