11a. Construct a Triangle Given the Lengths of Two Sides and the Bisector of Their Included Angle

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This Demonstration shows a construction of a triangle given the lengths of the sides and and the length of the angle bisector of .

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Construction

Draw the line segment of length , and let be on the perpendicular to at such that .

Step 1: Construct the inscribed square of the triangle.

Then satisfies the conditions.

Verification

Let the point be the fourth point of the rhombus . In any triangle , the inscribed rhombus has side length , which is independent of .

By construction, and .

Since and is a diagonal of the rhombus , is the angle bisector of at of length .

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Contributed by: Izidor Hafner (August 2017)
Open content licensed under CC BY-NC-SA


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Reference

[1] D. S. Modic, Triangles, Constructions, Algebraic Solutions (in Slovenian), Ljubljana: Math Publishers, 2009 pp. 44.



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