Construction of Polygons — Important Questions

Two consecutive sides and included angle, One side and both diagonals, Two diagonals and included angle, Two adjacent sides and height

Multiple methods exist for parallelogram construction: (1) Two consecutive sides + included angle, (2) One side + both diagonals, (3) Two diagonals + included angle, (4) Two adjacent sides + height. Four sides alone are insufficient as opposite sides are automatically equal in a parallelogram.

Using interior angles of 120°, Using circumcircle with radius equal to side, Using central angles of 60°

Three methods exist: (1) Using 120° interior angles, (2) Circumcircle method where radius = side length, (3) Central angle method using 60° angles (360°/6). Ruler alone cannot construct accurate regular hexagon.

60°

For any regular polygon, central angle = 360°/n. For hexagon, n = 6, so central angle = 360°/6 = 60°. This is why the circumcircle construction method works using 60° angles.

True

A square is a special rhombus where all sides are equal and all angles are 90°. Since a square's diagonals are equal and bisect each other at right angles (like a rhombus), the same diagonal construction method applies.