In triangle ABC, D is the mid-point of BC. If DL is perpendicular to AB and DM is perpendicular to AC such that DL = DM, then the triangle will be:

Question

Accepted Answer

Given triangle ABC with D as the midpoint of BC, DL is perpendicular to AB and DM is perpendicular to AC, and DL = DM.

Step 1: Since D is midpoint of BC, BD = DC.

Step 2: DL and DM are perpendiculars from D to sides AB and AC respectively.

Step 3: DL = DM implies the distances from D to AB and AC are equal.

Step 4: This equality of perpendicular distances from the midpoint of BC to sides AB and AC implies that AB = AC because the point D lies on BC and the perpendicular distances to AB and AC are equal.

Step 5: Hence, triangle ABC has AB = AC, which means it is an isosceles triangle.

Therefore, the triangle will be isosceles.

Answer

Answer

Answer