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.
Given: In ΔABC, AB = AC
and D and E are mid point of AB and AC
⇒ AD = BD = AE = CE .....(1)
In ΔABC
∠ABC = ∠ACB (Angles opposite to equal sides)
⇒ ∠DBC = ∠ECD ......(2)
Now, In ΔDBC and ΔECB
DB = EC (From (1))
∠DBC = ∠ECD (From (2))
BC = CB (Common)
So, ΔDBC ΔECB (By SAS congruency criterion)
⇒ BE = CF (CPCT)