Question

The figure above the design of a circular stained-glass panel. The 2 squares shown are inscribed in the circle. All are triangular pieces shown are congruent and have a common vertex with each adjoining triangular piece. The diameter of the panel is 2 feet.
Find the number of lines of symmetry in the design of the stained-glass panel.

Answer 1

Hint: So, students here in this question we have to find the number of the symmetry in the design of the stained-glass panel if a figure is rotated by ${{45}^{0}}\left( {{\dfrac{1}{8}}^{th}}of{{360}^{0}} \right)$then the outline of this figure fits its own outline. That’s why we will find the rotational symmetry of order that is 8 in this problem the order is 8. For this problem, we need the imagination that the only way we can solve this problem.

Complete step-by-step solution:

The figure given below is the design of a circular stained-glass plane hope’s well antique shop seems Separate the pieces of the panel all red triangular prices are shown are congruent and have a common vertex with each adjoining triangular piece two square shown is inscribed in the circle the diameter of the panel is two feet, so we have all this information describing. The diagram here the question says the design of the stained glass panel has how many lines of symmetry in the plane of the panel so what does a line of symmetry means basically it means that if you were to draw a line through the figure you had have mirror images on either side of that lines so far example if I drew a line directly down the center of the circle, it’s not perfectly straight then I have mirror images on both sides of that line I can also get mirror images by drawing really through any diagonal through these vertexes. So, by the diagram, the mirror image will be \[4\times 2=8\].
So, the line of symmetry in the design of the stained-glass panel is 8.

Note: Here to solve this problem first you need to draw the symmetry of lines to get the number of lines of symmetries we divide the figure as shown below:

There is a total of 8 lines that don’t get confused between 16 and 8 because when we count circular that will make a count of 16 so take care of it.
Hence the number of lines of symmetry is 8 as shown in the figure.