Draw a rough sketch of a regular hexagon. Connecting three of its vertices draw:

(i) an isosceles triangle

(ii) a right-angled triangle.

A regular hexagon has 6 equal sides and 6 equal interior angles.

(i) Isosceles triangle: Connecting vertices A, B and C of the hexagon ABCDEF, we get triangle ABC in which two sides are equal. So, ABC is an isosceles triangle.

(ii) Right-angled triangle: Connecting vertices A, B and D of hexagon ABCDEF (where AD is a diameter of the hexagon).

As we know that all interior angles of a regular hexagon = 120°. Since, all sides of a regular hexagon are equal that means BC = CD, therefore, BCD is an isosceles triangle,

$\Rightarrow$ ∠CBD = ∠CDB (Angles opposite to equal sides are equal)

As this is a regular hexagon, ∠C = 120°

Now sum of all angles of triangle BCD,

∠CBD + ∠CDB + ∠C = 180°

2∠CBD + 120° = 180°

2∠CBD = 180° - 120° = 60°

∠CBD = 30°

As, ∠ABD + ∠CBD = ∠B = 120°

∠ABD + 30° = ∠B = 120°

∠ABD = 120° - 30°

∠ABD = 90°

So, we get a right-angled triangle ABD with the right angle at B.