Construction 6: To construct a triangle, given its perimeter and its two base angles.
Steps of Construction:
- Draw a line segment, say XY equal to BC + CA + AB.
- Make angles LXY equal to ∠B and MYX equal to ∠C.
- Bisect ∠LXY and ∠ MYX. Let these bisectors intersect at a point A .
- Draw perpendicular bisectors PQ of AX and RS of AY.
- Let PQ intersect XY at B and RS intersect XY at C. Join AB and AC . Then ABC is the required triangle.