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ACB and DCB are on same base BC
AB= BC
BD =CD
AD = AD
triangle ABD congruent to triangle ACD ( by SSS Congruence rule
therefore. angle BAE = angle CAE ( By cpct )
- In triangle BAE and triangle ACE
- AB =AC
- AE =AE
- angle BAE = angle CAE
- therefore triangle BAE = Triangle ACE ( by SAS congruence rule )
- therefore angle BEA = angle CEA and BE=CE ( by cpct )
- angle BEA + angle CEA = 180 ( linear pair )
- 2angle BEA = 180
- angle BEA = 90
- angle BEA = angle CEA = 90
- hence AD bisect the base BC at right angle
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