Question

What are the conditions to be satisfied for the construction of a triangle when perimeter and base angles are given?

Answer 1

Construction of $\Delta ABC$, given the perimeter (AB + BC + CA) = 'a' cm, $\angle B=x^{\circ }$ and $\angle C=y^{\circ }$.
Steps of construction:
Step 1: Draw the line segment XY = 'a' cm
Step 2: Draw the ray XL at X making an angle of $x^{\circ }$ with XY
Step 3: Draw the ray YM at Y making an angle of $y^{\circ }$ with XY
Step 4: Draw angle bisector of $\angle LXY$.
Step 5: Draw angle bisector of $\angle MYX$ such that it intersects the angle bisector of $\angle LXY$ at a point A.
Step 6: Draw the perpendicular bisector of AX such that it intersects XY at a point B.
Step 7: Draw the perpendicular bisector of AY such that it intersects XY at a point C.
Step 8: Join AB and AC
Thus, ABC is the required triangle.