Ok, Let me start from the word Similar , the word which is usually used in mathematics for geometrical shapes mainly polygons.
Similar Polygons= Two or more Polygons are said to be similar if their corresponding sides are proportional and Corresponding interior angles are equal.
I will answer this question by starting from
1. Option A:→ Trapezoids= Why two trapezoids can't be similar because if we consider parallel sides of trapezoids their length can vary. Suppose One trapezoid has parallel sides of length 7 m and 13 m , and other trapezoid has parallel sides of length 6 m and 11 m.So, neither the corresponding sides are proportional nor interior angles are equal.
So, the Statement is Incorrect that All Trapezoids are always similar to one another.
2. →B.isosceles triangles=One isosceles triangle (4,4,5, 50°,50°,80°) and Other isosceles triangle being (3,3,7,55°,55°,70°).
So, the Statement is Incorrect that All Isosceles triangles are always similar to one another.
3. →→C.Equilateral triangles=All equilateral triangles will always be similar because their all interior angles will always be 60°, whatever the length of their sides.So, two equilateral triangles will always be similar because ratio of their corresponding sides will always be equal and their corresponding interior angles will always be 60°.
4. →→D.Rectangles= Consider two rectangles having Dimensions (70 × 40) and (60 × 30).
So, the Statement is Incorrect that All Rectangles are always similar to one another.
5.→→E. Pentagons :=Two Regular pentagons are always similar to each other, but not all.
So, the Statement is Incorrect that All Pentagons are always similar to one another.
Option C i.e Set of equilateral triangles, is true statement about the set of shapes which contains members that are always similar to one another.
