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10. Construct a Triangle Given the Length of Its Base, the Difference of the Base Angles and the Slope of the Median to the Base

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This Demonstration shows a construction of a triangle given the length of the base , the difference of the base angles and the slope of the median from to the base.

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Construction

Draw a segment of length with midpoint .

Step 2: Draw a circle with center and radius . Let and be intersections of and .

Step 3: Let be the intersection of and the line through parallel to .

Verification

Let and .

By construction, the triangles and are similar, so . The line segment is the median of with slope since is on and is the midpoint of .

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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. 91.

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