In the given figure, D is the midpoint of BC, DE ⊥ AB and DF ⊥ AC such that DE=DF. Then, which of the following is true?

Question

Philoid · Accepted Answer

From the given figure, we have

D is the mid-point of BC

Also, DE is perpendicular to AB

DF is perpendicular to AC

And, DE = DF

Now, in ∆BED and ∆CFD we have:

DE = DF

BD = CD

∠E = ∠F = 90^o

∴ By RHS congruence rule

∆BED ≅ ∆CFD

Thus, ∠B = ∠C

AC = AB

Hence, option (A) is correct