# 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:

**Explanation:**

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]