Question

In figure, BD and CEy are altitudes of ∆ABC and ∆BD = CE.

(i) Write three pairs of equal parts in ∆CBD and ∆BCE.

(ii) Is ∆CBD ≅ ∆BCE ? Why and why not?

(iii) Is ∠DCB ≅ ∠EBC ? Why and why not?

Answer 1

(i) Three equal parts in ∆CBD and ∆BCE are

CB = BC (common)

∠CDB = ∠BEC (each 90°)

and BD = CE (given)

(ii) From R.H.S. condition of congruency

∆CBD ≅ ∆BCE

(iii) Yes, ∠DCB = ∠EBC

(∵ corresponding angles of congruent triangles are equal)