31. Construct a Triangle ABC Given the Length of AB, an Adjacent Angle and the Difference of the Lengths of the Other Two Sides

This Demonstration shows how to construct a triangle given the length of the side , the adjacent angle at and the difference of the lengths of the other two sides .

Construction

1. Draw the segment of length .

2. Draw a point so that .

3. Let be the intersection of the ray and the perpendicular bisector of .

4. Then is the required triangle.

Verification

Since the triangle is an isosceles triangle with apex , .