Math, asked by birjuthakur541, 5 months ago

10. In the adjoining figure, tringle 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 tringle BCF
= CBE.​

Answers

Answered by sumitpal123005
0

Answer:

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Answered by shalinithore100
4

Step-by-step explanation:

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.

ΔBCF≅ΔCBE.

∴ since ΔBCF≅Δ CBE, by properly of congruncy we can with that

BE = CF.

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