Congruency, SMB-007

In the figure below, \(AB \parallel DE, \ AC = CE\) and the line \(AE\) intersects \(DB\) at \(C\).

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

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\( \angle ACB = \angle DCE\ \ \text{(vertically opposite)} \)

\(AC = CE\ \ \text{(given)} \)

\(\angle BAC = \angle DEC\ \ \text{(alternate,}\ AB \parallel DE \text{)} \)

\(\therefore\ \Delta ABC \equiv \Delta EDC\ \ \text{(AAS)}\)