if BC = 2AB, then compute B'C'/A'B'
To compute B'C'/A'B', we first need to understand the given information. BC = 2AB means that the length of BC is twice the length of AB.
Now, let's consider a diagram to better understand the problem. Let B, C, A, B', and C' be points on a line segment in that order. Let AB = x and BC = 2x.
The ratio B'C'/A'B' can be computed using the properties of similar triangles. In this case, we have two similar triangles, ABC and A'B'C', since both triangles have the same angle measures.
By considering the properties of similar triangles, we can say that corresponding sides of similar triangles are proportional. This means that B'C'/AB = A'C'/AC and A'B'/BC = A'C'/AC.
Since B'C' and A'B' share the same length, we can simplify the ratio as follows:
B'C'/A'B' = B'C'/BC = AC/A'C'
From the given information, we know that BC = 2AB, which means BC = 2x, and AC = AB + BC = x + 2x = 3x.
Using these values in the ratio:
B'C'/A'B' = B'C'/BC = AC/A'C' = 3x/2x = 3/2
Therefore, B'C'/A'B' = 3/2.