Question

In a triangle, the perpendicular from the vertex to the base bisects the base. The triangle is ______.

Options

• right-angled

• isosceles

• scalene

• obtuse-angled

Answer 1

In a triangle, the perpendicular from the vertex to the base bisects the base. The triangle is isosceles.

Explanation:

Let the triangle be ABC with AD ⟂ BC and D the midpoint of BC.

Triangles ABD and ACD are right-angled, with AD common and BD = DC, so the two triangles are congruent and hence AB = AC.

Therefore, the triangle is isosceles.