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5.5 Angle bisector theorem

In a triangle the angle bisector divides the opposite side in the ratio of the remaining sides. This means that for a D ABC ( figure 5.5) the bisector of Ð A divides BC in the ratio .

Figure 5.5

To prove that

Through C draw a line parallel to seg.AD and extend seg.BA to meet it at E.

seg.CE çç seg.DA

Ð BAD @ Ð AEC , corresponding angles

Ð DAC @ Ð ACE , alternate angles

But Ð BAD = Ð DAC , given

\ Ð AEC @ Ð ACE

Hence D AEC is an isosceles triangle.

\ seg.AC @ seg.AE

In D BCE AD çç CE

Thus the bisector divides the opposite side in the ratio of the remaining two sides.

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Index

5.1 Introduction
5.2 Ratio And Proportionality
5.3 Similar Polygons
5.4 Basic Proportionality Theorem
5.5 Angle Bisector Theorem
5.6 Similar Triangles
5.7 Properties Of Similar Triangles

Chapter 6

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