Mathematics of the second day of junior high school about isosceles triangle

Solution: (1)∵AB=AC, AD=AE, ∠ BAC = ∠ DAE = 60,

∴△AED and △ABC are equilateral triangles,

∴∠C=∠ABC=60，∠EAB=∠DAC

∴△EAB≌△DAC，

∴∠EBA=∠C=60，

∫EF∨BC，

∴∠EFB=∠ABC=60，

∵ In △EFB, ∠ EFB = ∠ EBA = 60,

∴△EFB is an equilateral triangle,

(2)①△BEF is an isosceles triangle,

AB = AC，AD=AE，∠BAC=∠DAE，

∴△AED and △ABC are isosceles triangles,

∴∠C=∠ABC,∠EAB=∠DAC，

∴△EAB≌△DAC，

∴∠EBA=∠C，

∫EF∨BC，

∴∠EFB=∠ABC，

∵ in △EFB∠EFB =∠EBA,

∴△EFB is an isosceles triangle,

②AB=AC, and point D is a moving point on ray BC (not coincident with B and C). Take AD as one side and make △ADE on the left side of AD, so that AD=AE, ∠DAE=∠BAC, the parallel line passing through point E is BC, and the intersection AB is at point F, connecting Be.

∵△BEF is an isosceles triangle,

AB = AC，AD=AE，∠BAC=∠DAE，

∴△AED and △ABC are isosceles triangles,

∴∠ACB=∠ABC,∠EAB=∠DAC，

∴△EAB≌△DAC，

∴∠EBA=∠ACD，

∴∠EBF=∠ACB，

∫EF∨BC，

∴∠AFE=∠ABC，

∠∠ABC =∠ACB，

∴∠AFE=∠ACB，

∵ In △EFB∠EBF =∠AFE,