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geometry intermediate

Problem

In the diagram, the two triangles shown have parallel bases. What is the ratio of the area of the smaller triangle to the area of the larger triangle? Express your answer as a common fraction.
problem
Solution
Because of our parallel bases, we can see that corresponding angles of the triangles must be congruent. Therefore, by AA similarity, we see that the two triangles are similar.

If two similar triangles have side ratios of the ratio of their areas must be In our diagram, we see that the ratio of the sides of the smaller triangle to the sides of the larger triangle is Therefore, the ratio of the areas is the square of that, or
Final answer
\dfrac{4}{25}