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E and F are respectively the mid-points...

E and F are respectively the mid-points of equal sides AB and AC of `DeltaA B C`(see Fig. 7.28). Show that BF = C E`.

Text Solution

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Given `E` and `F` are mid point of equal sides `AB` and `AC` of `triangle ABC`
In `ΔABF and ΔACE`
`AB=AC` (given )
`∠A=∠A` (common angle )
`AF=AE` (halves of equal sides)
∴`ΔABF≅ΔACE` (SAS rule)
∴`BF=CF` (CPCT)
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