Question

In Fig,

BD and CE are altitudes of ∆ABC such that BD = CE.
(i) State the three pairs of equal parts in ∆CBD and ∆BCE.
(ii) Is ∆CBD ≅ ∆BCE? Why or why not?
(iii) Is ∠DCB = ∠EBC? Why or why not?

Answer 1

(i)
In ∆CBD and ∆BCE,
∠D = ∠E = 90°
Side BC = Side BC
Side BD = Side CE.

(ii) ∆CBD ≅ ∆BCE.........[From (i), RHS Congruence Criterion]
(iii) ∠DCB = ∠EBC.......(Corresponding Angle Congruence Test)