It is proved that: ad = CD = ab

Well, it seems to be proof: ad = CD + ab
Proof: do me ⊥ ad through M
Because DM bisects ∠ ADC, so ∠ CDM = ∠ EDM ①
And ∠ DCM = ∠ DEM = 90 °, then ∠ DME = ∠ DMC ②
The common side is DM
So ⊿ CDM ≌ EDM (ASA)
So de = DC, CM = em
And M is the midpoint of BC, so BM = cm = em
And ∠ AEM = ∠ ABM = 90 °, am is the common edge
So ⊿ AEM ≌ ABM (HL)
So AE = ab
So CD + AB = de + AE = ad
The original proposition is proved

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