Is the similarity ratio between the three triangles equal to one?
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Is the similarity ratio between the three triangles equal to one?
To answer the question, we first need to understand what "similarity ratio" means.
In similar triangles, the ratio between the sides is constant.
In the statement, we do not have data on any of the sides.
However, a similarity ratio of 1 means that the sides are exactly the same size.
That is, the triangles are not only similar but also congruent.
In the drawing, you can clearly see that the triangles are of different sizes and, therefore, clearly the similarity ratio between them is not 1.
No
If it is known that both triangles are equilateral, are they therefore similar?
A similarity ratio of 1 means the triangles are congruent - they have exactly the same size and shape! This is much stronger than just being similar.
Visual inspection can help! If triangles have the same angles but clearly different sizes (like nested triangles), they're similar but not congruent.
Each pair of similar triangles has one specific similarity ratio. If you're comparing three triangles, you get three different ratios: A:B, B:C, and A:C.
Look at the diagram! The outer triangle is clearly larger than the inner ones. If the ratio were 1, all triangles would be exactly the same size - which they're not!
Similar: same shape, possibly different size. Congruent: same shape and same size. Congruent triangles are similar with ratio = 1.
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