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Right angle triangles
Right triangles - those with a 90-degree angle.
Triangles do not have parallel lines but as right angles triangles they do have perpendicular lines that meet at 90 degrees.
There are many uses of similar triangles in daily life. These triangles can create the symmetry in art and other aspects that they enjoy.
The HA and HL theorems for right triangles or the Pythagorean theorem might be of use.