9. Construct a Triangle Given the Length of Its Base, the Difference of the Base Angles and the Sum of the Other Two Sides
This Demonstration shows a construction of a triangle given the length of the base , the sum of the other two sides and , and the difference of the base angles.[more]
Draw a line segment of length .
Step 1: Draw a circle with center so that the central angle . Measure out the point on at distance from .
Step 2: Let the point be the intersection of the perpendicular bisector of and .
Let , and .
Since by construction, . On the other hand, , so . Since is isosceles, . By construction, .[less]