Question

$\text{In the given figure, if x = y and AB = CB then prove that AE = CD.}$

Answer 1

Consider the triangles AEB and CDB.
∠EBA=∠DBC (Common angle) ...(i)
Further, we have:
∠BEA=180-y
∠BDC=180-x
Since x = y, we have,180-x =180-y
⇒∠BEA=∠BDC ...(ii)
AB = CB (Given) ...(iii)
From (i), (ii) and (iii), we have:
△AEB ≅△CDB (AAS criterion)
∴ AE = CD (CPCT)
Hence, proved.