Question

Construct a regular hexagon of side 3.5 cm and draw all its lines of symmetry.

Answer 1

Given: Construct a regular hexagon of side 3.5 cm and draw all its lines of symmetry.

Steps of construction:

1. Draw a line segment AB = 3.5 cm.
2. With A as center and radius 3.5 cm, draw an arc.
3. With B as center and radius 3.5 cm, draw another arc intersecting the first arc at point C.
4. Using the compass set at 3.5 cm, step around the circle drawing arcs from each new point to mark off the six vertices of the hexagon.
5. Join the six points in order to construct the regular hexagon ABCDEF, each side measuring 3.5 cm.
6. To draw the lines of symmetry of the regular hexagon, note that a regular hexagon has 6 lines of symmetry:
   • 3 lines pass through the opposite vertices.
   • 3 lines pass through the midpoints of opposite sides.
7. Draw straight lines connecting opposite vertices A to D, B to E, C to F.
8. Draw straight lines connecting midpoints of opposite sides.

We have constructed a regular hexagon ABCDEF with each side measuring 3.5 cm. All six lines of symmetry have been drawn, consisting of three lines through opposite vertices and three lines through midpoints of opposite sides.