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 [tex]\frac{AD}{AB}=\frac{DC}{CB}[/tex]
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.
[tex]\frac{DE}{EB}=\frac{AD}{AB}[/tex] → (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.
[tex]\frac{DE}{EB}=\frac{CD}{CB}[/tex] → (2)
From equation (1) and (2), we get
[tex]\frac{AD}{AB}=\frac{CD}{CB}[/tex]
Hence Proved.
