| Proposed
Problem 4 How many similar triangles can be obtained by joining the midpoints of the sides of a triangle? Conjecture There are five similar triangles. The four triangles obtained by joining the midpoints of a triangle are similar to each other, and each one of them is similar to the original triangle. i.e. △ DBE ∼ △ FEC ∼ △ ADF ∼ △ EFD ∼ △ ABC A parallel to a side of a triangle that intersects the other two sides cuts off a triangle similar to the original triangle. Congruent triangles are similar. |