In triangle ABC, D is the midpoint of BC. If DL is perpendicular to AB and DM is perpendicular to AC such that DL = DM, then the triangle will be:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. isosceles triangle.
BD = CD and DL = DM
DL ⊥ AB and DM ⊥ AC
In ΔBDL and ΔCDM,
BD = CD; DL = DM; and ∠BLD = ∠CMD = 90°
ΔBDL ≅ ΔCDM [RHS]
So, ∠DBL = ∠DCM
Then, AB = AC
Therefore, the ΔABC will be an isosceles triangle.