It is proved that the similar process can deduce the relationship of angles according to the relationship of edges. These two triangles are isosceles triangles with a vertex angle of 36 degrees, that is, golden triangles.
AB:BC=BC:CD
CD=AC-AD=AB-BC
So AB:BC=BC:(AB-BC)
Solve equation BC=(3√5)-3.
(2) Yes ~ Because BC:AB=(AB-BC):BC, this is the definition of the golden section.
(3)AD=BC, in the Golden Triangle ABC, the ratio of BC to waist AC is the golden ratio, so
The ratio of AD to AC is also the golden section ratio, that is, D is the golden section point of AC.