Property of Internal Angle Bisector - Hubert Shutrick's PWW

Let \(AD\) be an angle bisector in \(\Delta ABC\),

property of internal angle bisector

Then \(\displaystyle\frac{b}{c}=\frac{a_{b}}{a_{c}}\), where \(b=AC\), \(c=AB\), \(a_{b}=CD\), \(a_{c}=BD\).

(The applet below illustrates a proof by Hubert Shutrick. Points \(A\), \(B\), \(C\), \(A'\) are draggable.

Proof

This proof without words is due to Hubert Shutrick.

property of internal angle bisector - PWW

This is another example showing how the product identities that you get algebraically from similar triangles can be illustrated. The method applies in several additional situations.

(There are several theorems that are proved by similar technique.)


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