Question

In \( \triangle ABC \) and \( \triangle DEF , AL \perp BC , DM \perp EF , AB = DE , AC = DF , AL = DM \). Show that \( \triangle ABC \cong \triangle DEF \),

Answer 1

In triangles Δ ABL & Δ DEM, 

∠ALB = ∠DME = 90°

AB = DE (Given)

AL = DM (Given)

∴ ΔABL ≅ ΔDEM (By RHS congruent criteria)

∴ ∠ABL = ∠DEM---(1) (By property of congruent triangles)

Similarly, ΔACL ≅ ΔDFM

and ∠ACL = ∠DFM---(2)

Now, in triangle ΔABC and ΔDEF,

∠ABL = ∠DFM (From (1))

∠ACL = ∠DFM (From (2))

∴ ΔABC ≅ ΔDEF (By AAS congruent criteria)