In the given figure, ABC is an isosceles triangle in which AB=AC. If E and F be the midpoints of AC and AB respectively, then BE is equal to _______.
A
CF
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B
AB
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C
CE
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D
BF
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Solution
The correct option is ACF Since, AB=AC ⇒12AB=12AC ⇒BF=EC Also, AB=AC
⇒∠B=∠C [Angles opposite to equal sides are equal] In △BEC and △CFB, we have EC=FB .....(proved above) ∠B=∠C ....(proved above) BC=BC .....(common) ∴△BEC≅△CFB ......(By SAS) ⇒BE=CF .....(By CPCT)