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In the adjoining figure, ABC is an isosceles triangle in which AB = AC. If E and F be the midpoints of AC and AB respectively, prove that BE = CF. Hint. Show that ,BCF CBE.
1386275_b52e1e33f54c4632839bc175f73dd132.PNG

Solution
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Given Δ is an isosceles triangle
AB-BC _______(1)
and B=C ________(2)
Here E andF are midpoints of AC and AB respectively
AF = FB and AE = EC
know , AB = BC
AF+FB = AE + EC
2AF = 2AE
AF = AE.
AF =FB = AE =EC _______(3)
In ΔBCF and Δ CBE
BC = BC [common side]
B=C [from (2)]
BF = EC [from (3)]
By SAS condition for congruency.
ΔBCFΔCBE.
since ΔBCFΔ CBE, by properly of congruncy we can with that
BE = CF.

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