Congruency, SMB-005

In the figure below, \(BE = BC\), \(AB = BD\) and the line \(AD\) intersects \(CE\) at \(B\).

Prove that this pair of triangles are congruent. (2 marks)

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\( \angle ABE = \angle CBD\ \ \text{(vertically opposite)} \)

\(AB = BD\ \ \text{(given)} \)

\(EB = BC\ \ \text{(given)} \)

\(\therefore\ \Delta ABE \equiv \Delta DBC\ \ \text{(SAS)}\)