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Angle Bisector theorem

Mathematics 3. 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  . To prove that 

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Angle Bisector theorem

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  1. Mathematics 3 Angle Bisector theorem

  2. 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 .

  3. To prove that  Through C draw a line parallel to seg.AD and extend seg.BA to meet it at E. seg.CEççseg.DA РBAD @ Ð AEC , corresponding angles РDAC @ 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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