The angle ABC is an equilateral triangle, CE bisects the angle ACF, D is a point on BC, and the angle ade = 60 ° proves ad = De The angle ACF is the outer angle of an equilateral triangle

Intercept AF = CD on AB and connect FD
Because the angle abd = angle ade = 60 degrees, the angle ADC = abd + bad, the angle bad = angle EDC
Because AB = BC and AF = CD
So ab-af = bc-cd
That is BF = BD
So triangle BDF is equilateral triangle,
So the angle AFD = angle DCE = 120 degrees
In triangular AFD and DCE
DAF = EDC, AF = DC, AFD = DCE,
So the triangle AFD is equal to the triangle DCE
So ad = De,

RELATED INFORMATIONS

1. As shown in the figure, triangle ABC is an equilateral triangle, D is a point on BC, angle ade = 60 degrees, CE bisects the outer angle ACF of triangle ACB, proving: ad = De
2. In the triangle ABC, the angle ACB is equal to 90 degrees, the points E and F are on the edge AB, and the angle CEB = angle ECB, the angle CFA = angle FCA, and the degree of the angle ECF is calculated
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