Question

In the adjoining figure, triangle 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 triangle BCF congruent to triangle CBE.
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Answer 1

Answer:

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.

ΔBCF≅ΔCBE.

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

BE = CF.

solution