Known: as shown in the figure, ad = AE, ab = AC, ∠ DAE = ∠ BAC

Known: as shown in the figure, ad = AE, ab = AC, ∠ DAE = ∠ BAC

It is proved that: in ∵ bad and △ CAE, ad = AE, bad = caeab = AC, bad = SAS and BD = EC

As shown in the figure, after rotating △ ABC clockwise about its vertex a for 30 ゜, we get △ AEF. (1) what is the relationship between △ ABC and △ AEF? (2) Find the degree of ∠ EAB; (3) when △ ABC rotates clockwise about its vertex a, the vertex F of △ AEF after rotation and the vertices C and a of △ ABC are on the same line?

(1) ∵ rotate △ ABC clockwise about its vertex a for 30 ゜, and get △ AEF, ≌ ABC ≌ AEF. (2) ∵ rotate △ ABC clockwise about its vertex a for 30 ゜, and get △ AEF, ∨ EAB = 30 ゜ (3) ∵ if △ ABC rotates clockwise about its vertex a, the vertex F of △ AEF after rotation and the vertices C and a of △ ABC are on the same straight line, ∨ CAF = 180 ° and ゜ ．

As shown in the figure, it is known that △ ABC and △ ade are equilateral triangles, connecting CD and be

It is proved that ∵ ABC and ∵ ade are equilateral triangles, ∵ AB = AC, AE = ad, ∵ DAE = ∵ cab, ∵ Dae - ∵ CAE = ∵ Cab - ∵ CAE, ∵ DAC = ∵ EAB, in △ ADC and △ AEB, ad = AE