From each vertex to its opposite vertex. These will be centered on a shared point at the center of the hexagon. Each complete line will be a line of symmetry for the hexagon.
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For a regular pentagon, draw a segment from each vertex to the midpoint of the side length directly opposite, there by cutting it in half.
In general it cannot be done. In the rare case that the hexagon is regular, select three alternate vertices and draw lines to the centre (centroid) of the hexagon. These will form three congruent rhombi.
Start by drawing a regular hexagon.Now move one of the vertices either a little way towards, or away from the centre of the hexagon, and redraw the lines joining it to its neighbour vertices.To construct using a straight edge and a compass:Construct a regular hexagon:Draw a circle; call its centre O.Mark a point on the circumference of the circle.Keeping the compass set to the same width (the radius of the circle), draw an arc to intercept the circle with the centre on the marked point.Repeat step 3 using the last arc-circumference intercept as the centre for the next arc until 6 marks have been made.Label the marks in the order they were drawn A, B, ..., FDraw in only the lines BC, CD, DE, EF (that is miss out lines AB and FA which would complete the regular hexagon).Draw in the line AOD (if the vertices were marked properly in construction, these will lie on a diameter of the circle) and extend it either side of the circle.Mark a point beyond A on AOD and call it G.Draw in lines GB and FG.Hexagon GBCDEF is an irregular hexagon with one line of symmetry, namely GAOD.
For a picture of a rectangle with the lines of symmetry drawn, see the Related Link below. The image is toward the bottom of the page.
Draw lines from every other angle that meet in the center.