Determining symmetry groups ongeometric builds using reflection and rotation tests

This research is motivated by the researcher’s desire to see the folding and rotational symmetry in geometric shapes whether they meet the symmetries for certain aspects and form a group. The method used in testing the symmetry of a group in geometric shapes is by testing reflection and rotation with a combination of linear and abstract algebra using an ordered matrix, where the geometric shapes are traced on each particular aspect until they meet the symmetry. From the results of the method used, it is found that the triangles to the octagon groups are symmetrical through the test of rotation and reflection of the geometric shapes. Thus, it can be concluded that group symmetry occurs up to the order of eight in geometric shapes. Based on the pattern, starting from the pentagon it is not a symmetry group, the hexagon includes the symmetry group, the heptagon is not a symmetry group, the octagon includes a symmetry group, then the nonagon is not a symmetry group and the decagon belongs to the symmetry group