Question

In the figure given below AABC, D is the midpoint of BC. DE ⊥ AB, DF ⊥ AC and DE = DF. Show that ΔBED ≅ AΔCFD.

Answer 1

Given that D is the mid point of BC of ΔABC. 

DF ⊥ AC; DE = DF 

DE ⊥ AB 

In ΔBED and ΔCFD 

∠BED = ∠CFD (given as 90°) 

BD = CD (∵D is mid point of BC) 

ED = FD (given) 

∴ ΔBED ≅ ΔCFD (RHS congruence)