Download Angle Bisector Theorem (notes)

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Transcript
GEOMETRY
Notes: Angle Bisector Theorem
Notes:
Angle Bisector Theorem
In a triangle the angle bisector divides the opposite side in the ratio of the remaining sides. This
ABC ( figure 5.5) the bisector of 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
seg.DA
BAD
AEC , corresponding angles
DAC
ACE , alternate angles
But BAD = DAC , given
AEC
ACE
Hence AEC is an isosceles triangle.
seg.AC seg.AE
Instructor: CHRISTLE MAE B. OCHIGUE
[email protected]
In BCE AD
CE
Thus the bisector divides the opposite side in the ratio of the remaining two sides.
Source: http://www.pinkmonkey.com/studyguides/subjects/geometry/chap5/g0505501.asp
Instructor: CHRISTLE MAE B. OCHIGUE
[email protected]