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s2008m [1.1K]
3 years ago
13

Suppose given △ABD and △CBD.

Mathematics
1 answer:
patriot [66]3 years ago
5 0

Answer:

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 \frac{AD}{AB}=\frac{DC}{CB}

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.

\frac{DE}{EB}=\frac{AD}{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.

\frac{DE}{EB}=\frac{CD}{CB}    →  (2)

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

\frac{AD}{AB}=\frac{CD}{CB}

Hence Proved.

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