Suppose given △abd and △cbd. suppose ae and ce are angle bisectors. prove that ad ab = dc cb .

The required result is proved with the help of angle bisector theorem.

Step-by-step explanation:

Given △ABD and △CBD, AE and CE are the angle bisectors. we have to prove that

Angle bisector theorem states that an angle bisector of an angle of a Δ divides the opposite side in two segments that are proportional to the other two sides of triangle.

In ΔADB, AE is the angle bisector

∴ the ratio of the length of side DE to length BE is equal to the ratio of the line segment AD to the line segment AB.

  →  (1)

In ΔDCB, CE is the angle bisector

∴ the ratio of the length of side DE to length BE is equal to the ratio of the line segment CD to the line segment CB.

   →  (2)

From equation (1) and (2), we get

Hence Proved.

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