If BD is both the altitude and median of Δ ABC then what kind of Δ is ABC?
A triangle is a polygon that has three sides, three edges and three vertices.
Answer: Δ ABC is an isosceles triangle.
Here's the detailed answer:
Median of a triangle is a line segment joining a vertex to the opposite side of the triangle dividing it into half whereas altitude of a triangle is a line perpendicular to the opposite side of the triangle.
Given that in Δ ABC, BD is both altitude and median.
⇒ BD ⊥ AC and AD = DC
∠ADB = ∠BDC = 90º [BD is an altitude]
Therefore, Δ BDC ≅ Δ ADB
⇒ BC = AB [Parts of congruent triangle are equal]