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Examples of junior high school mathematics triangle
Proof: in △AFD and △BAD, ∠ AFD = ∠ bad = 60.

∠ADF=∠BDA

So △AFD is similar to △BAD ∠ Abd = ∠ FAD.

In △ABD and △CAE, ∠ Abd = ∠ FAD.

∠BAD=∠ACE=60

AB=AC

So △ABD is equal to △CAE CE=AD.

Ad2 = AC ﹒ CD.

So AB/CE=AD/CD

∠AFD=∠C=60

So △ADF is similar to △CED's ∠ ADB = ∠ CDE.