Math Proof (On Synchronous Math Practice of Zhejiang Education Press)

Because AD AD, BE is the height on the side of BC and AC, and f is the midpoint of AB.

So DF and EF are the median lines on the hypotenuse of right angles △ABD and △ABE, respectively.

So df = ab/2, ef = ab/2.

So df = ef = 4.

Because h is the midpoint of DE.

Therefore, according to the nature of "Trinity": FH⊥DE

Because ∠ c = 60.

So ∠ DAC = 30.

So DC/AC = 1/2.

Similarly, EC/BC = 1/2.

So DC/AC = EC/BC

Because ACB = DCE = 60.

So △ CDE △ taxi

So DE/AB = DC/AC = 1/2.

Because ab = 8

So de = 4

So DH = eh = 2

So according to Pythagorean theorem FH = 2 √ 3.

Qiuna