Discussion
In triangles ABC and DEF; \(\angle B = 90^{\circ}\), BC = 8 cm, \(\angle A = 40^{\circ}\), DE = 8 cm, \(\angle F = 40^{\circ}\) and \(\angle E = 90^{\circ}\). Then, which of the following statements is true ?
Answer: D
The true statement is \(\Delta ABC \cong \Delta FED\), by AAS.
In triangle ABC, \(\angle B = 90^{\circ}\), \(\angle A = 40^{\circ}\), so \(\angle C = 50^{\circ}\), and BC (opposite A) is 8 cm. In triangle DEF, \(\angle E = 90^{\circ}\), \(\angle F = 40^{\circ}\), so \(\angle D = 50^{\circ}\), and DE (opposite F) is 8 cm.
Matching equal angles gives A with F, B with E and C with D, and the equal sides BC and ED are each opposite the 40° angle. Two angles and a non-included side are equal, so the triangles are congruent by AAS in the order ABC and FED.
RHS needs the hypotenuses to be equal, which is not given, and the correspondence DEF or DFE pairs unequal angles.
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