Figures are mathematically similar…
Two or more figures are similar when they share a scale factor, their corresponding angles are congruent, and they have a true proportion. They also have to have the same general shape so a triangle and a rectangle can’t be similar.
To find a scale factor you have to take two corresponding sides and divide the bigger one by the smaller one. The answer is the scale factor. To find a true proportion you have to take two side lengths from the two or more shapes that correspond to each other and make their measurements into a ratio. Then your cross multiply them and if they each equal the same thing they are similar. Finally to find the if the corresponding angles are congruent you find the corresponding angles and measure them with a protractor.
True or false…
Any two rectangles are similar?
False because their side lengths could possibly not share a true proportion which means they are not always similar. In order for them to be similar their side lengths need to share a true proportion. Also if this is true then that means they do not share a scale factor.
Any two equilateral triangles are similar?
True because in order to be an equilateral triangle you have to have the same length of all of your sides. That means that there is a true proportion and a scale factor. That also means that the corresponding angles are congruent.