Congruency, SMB-001

The diagram shows two right-angled triangles where \(\angle BAC = \angle BDC = 90^{\circ}\), and \(AB = BD\).

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

--- 4 WORK AREA LINES (style=lined) ---

Show Answers Only

\(\text{Proof (See Worked Solutions)}\)

Show Worked Solution

\(BC\ \text{(hypotenuse) is common} \)

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

\(\angle BAC = \angle BDC = 90^{\circ}\ \ \text{(given)} \)

\(\therefore \Delta ABC \equiv \Delta DBC\ \ \text{(RHS)}\)