Question

In the given figure, BA⊥AC, DE⊥DF, such that, BA = DE, BF = EC. Then, by which congruence rule is ∆ABC ≅ ∆DEF?


(2 marks)

Answer 1

Consider triangles ABC and DEF
BA = DE ----------(1) (0.5 mark)
BF = EC (adding FC both side)
BF + FC = EC + FC
BC = EF -----------(2) (0.5 mark)
$\angle$A = $\angle$D (each 90$°$) ----------(3)
$\Delta ABC\cong \Delta DEF$(By RHS criteria) (1 mark)

Therefore above triangles are congruent by RHS criteria.