Draw a rough sketch of a regular hexagon. Connecting three of its vertices draw:
(i) an isosceles triangle
(ii) a right-angled triangle.

Question

Draw a rough sketch of a regular hexagon. Connecting three of its vertices draw: (i) an isosceles triangle (ii) a right-angled triangle.

KnowledgeBoat · Accepted Answer

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, ∠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.

Mathematics

Draw a rough sketch of a regular hexagon. Connecting three of its vertices draw:
(i) an isosceles triangle
(ii) a right-angled triangle.

Polygons

Related Questions

Name each of the following polygons:

Draw a rough sketch of a pentagon and draw its diagonals.

Can you identify the regular quadrilateral?

What is the shape of
(i) your geometry box?
(ii) a brick?
(iii) a matchbox?
(iv) a drum?
(v) a playing die?
(vi) a sweet laddu?

Mathematics

Draw a rough sketch of a regular hexagon. Connecting three of its vertices draw:(i) an isosceles triangle(ii) a right-angled triangle.

Polygons

Related Questions

Name each of the following polygons:

Draw a rough sketch of a pentagon and draw its diagonals.

Can you identify the regular quadrilateral?

What is the shape of(i) your geometry box?(ii) a brick?(iii) a matchbox?(iv) a drum?(v) a playing die?(vi) a sweet laddu?

Draw a rough sketch of a regular hexagon. Connecting three of its vertices draw:
(i) an isosceles triangle
(ii) a right-angled triangle.

What is the shape of
(i) your geometry box?
(ii) a brick?
(iii) a matchbox?
(iv) a drum?
(v) a playing die?
(vi) a sweet laddu?