Ok I know that suppose in a triangle ABC , there's a cevian AD intersecting BC at D and dividing it in the ratio 4:5 so which implies that it divides Area of Triangle also in ratio 4:5 by that cevian. My Question is Do this Cevian divides angle A in the same ratio .
2026-03-27 07:14:55.1774595695
Do CEVIANS in Triangles divides the emerging angle in the same ratio as they do to the opposite side .
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If you consider say an equilateral triangle and the median from its vertex, you have a situation in which the ratio 1:1 holds both for the side and the angle. But then, keeping the foot of the median fixed, you can slightly turn your side around that point. One of the halves gets bigger and the other one gets smaller, so the ratio is not preserved, although you are preserving the ratio 1:1 for the angles.
Conclusion: the property does not hold.