Given: \overline{BD} \cong \overline{BE}, BD ≅ BE , \overline{DE} DE bisects \overline{AB} AB and \overline{DE} DE bisects \overline{BC}. BC . Prove: \overline{AB} \cong \overline{BC} AB ≅ BC .

Given:

DE bisects .

DE bisects .

To prove:

Proof:

DE bisects

Then, .         ...(i)

DE bisects .

Then, .           ...(ii)

We have,

       ...(iii)

Using (i), (ii) and (iii), we get

        ...(iv)

Adding (iii) and (iv), we get

Hence proved.

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step-by-step explanation: