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

This Demonstration shows an alternative construction of a triangle given the lengths of the sides and and the length of the angle bisector of .
Draw the line segment with interior point so that and .
Step 1: Draw parallel lines through and at an arbitrary angle . On the line through , measure out so that . Let be the intersection of and the parallel line through .
Step 2: Construct an isosceles triangle with base and a leg of length .
Step 3: Let be a point such that and . That is, is a parallelogram. Let point be the intersection of the lines and .
In the triangle , divides in the ratio . So is the bisector of the angle at .


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