Question

Suppose you have abc with ab = 5, bc = 7, and ca = 10, and also efg with ef = 900, fg = 1260, and ge = 1800. are these triangles similar, and if so, what is the scale factor?

Answer 1

SSS theorem: If two triangles have three pairs of sides in the same ratio, then the triangles are similar.

Write the ratio between the smallest sides, between the greatest sides and between the middle sides and compare the results:

1. $\dfrac{EF}{AB}=\dfrac{900}{5}=180;$
2. $\dfrac{EG}{AC}=\dfrac{1800}{10}=180;$
3. $\dfrac{GF}{CB}=\dfrac{1260}{7}=180.$

This gives you that

$\dfrac{EF}{AB}=\dfrac{EG}{AC}=\dfrac{GF}{CB}=180.$

By SSS theorem triangles ABC and EFG are similar with scale factor 180.