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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.
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Solution
In the triangle ABC it is given that
AB = AC, BE and CFare medians.
We have to show that BE CF
To show BF = CF we will show that ΔBFC ≅ ΔBEC
In triangle ΔBFC and ΔBEC
As AB = AC, so
∠FBC = ∠ECF .........(1)
BC=BC (common sides) ........(2)
Since,
AB = AC
`1/2 AB =1/2 AC `
As F and E are mid points of sides AB and AC respectively, so
BF = CE ..........(3)
From equation (1), (2), and (3)
ΔBFC and ΔBEC
Hence FC = BE Proved.
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