In equilateral triangle ABC, is de / / BC. Angle ade an equilateral triangle?

In equilateral triangle ABC, is de / / BC. Angle ade an equilateral triangle?

Of course, because of De / / BC, so ad: ab = AE: AC, and because AB = AC, so ad = AE, and angle a is 60 degrees, an isosceles triangle with an angle of 60 degrees is an equilateral triangle

As shown in the figure, in an equilateral triangle ABC with side length 4, ad ⊥ BC is at point D, and ad is taken as one side to make an equilateral triangle ade to the right. (1) find the area s of △ ABC; (2) judge the position relationship between AC and De, and give the proof

(1) In positive △ ABC, ad = AC × sin ∠ C = 4 × sin, 60 ° = 4 × 32 = 23, (2 points) ℅ s = 12bc × ad = 12 × 4 × 23 = 43. (3 points) (2) the positional relationship between AC and de: AC ⊥ de. (1 point) in △ CDF, ∵ CDE = 90 ° - ADE = 30 °, (2 points) ≠ CFD = 180 ° - C - ∠ CDE =