Find all theorems in junior high school mathematics (for geometric proof). . . All right, extra points. . - Training Enrollment Network

Find all theorems in junior high school mathematics (for geometric proof). . . All right, extra points. .

A: AE=EF

Proof: Make auxiliary line AC in the drawing.

Because ABCD is a square, CF is the bisector of ∠DCG outside the square.

So AC⊥CF and ∠ ECF = 45, which means that EC is the bisector of ∠ACF.

Because AE⊥EF, EC is also the bisector of ∠AEF.

So ∠ ECF = ∠ CEF = 45.

∠ EFC = 90, then EF=FC.

AE⊥EF

AC⊥CF

So AEFC is square, which means AE=EF.

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