Figures are mathematically similar when they share a scale factor and all corresponding angles are congruent. Having congruent corresponding angles on triangles will automatically be similar but since all rectangles and squares have 90 degree that’s where scale factor comes in. If a shape has all congruent corresponding angles and scale factor that means the similar shape is just an enlarged version of the original similar shape.
True or False, any two rectangles are similar: False. Even though all rectangles’ corresponding angles are congruent not all rectangles share a scale factor. Like I said before, for two shape to be similar they have to share a scale factor and all corresponding angles must be congruent.
True or False, any two equilateral triangles are similar: True. On triangles, if all corresponding angles are congruent it will ensure that those two riangles that have corresponding congruent angles will automatically share a scale factor. We know that all triangles’ angles add up to 180 degrees, which would mean that on all equilateral triangles, the three angles would all be 60 degrees (because the 180 has to be distributed evenly to all angles). Now, since we know that all angles on all equilateral triangles are the same, it tells that there will for sure be a scale factor.