如图1,在Rt△ABC和Rt△ADE中,AB=AC,AD=AE,角A=90度,M,N分别是EB,CD的中点

∵△ABC和△ADE为等边三角形
∴AB=AC,AE=AD,∠BAC=∠EAD=60°
∵∠BAE =∠BAC－∠EAC =60°－∠EAC,
∠DAC =∠DAE－∠EAC =60°－∠EAC,
∴∠BAE=∠DAC,
∴△ABE ≌ △ACD
∴CD=BE
∵M,N分别为EB,CD的中点
∴DN=1/2DC=1/2EB=EM
∵∠ADN=∠AEM,AD=AE
∴△ADN≌△AEM
∴AN=AM,∠DAN=∠EAM
∵∠DAE=∠DAN+∠EAN=∠EAM+∠EAN=∠MAN=60°
∴△AMN是等边三角形