Construction of Polygons
ICSE · Class 9 · Mathematics
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How many measurements are required to construct a quadrilateral when four sides and one angle are given?
In constructing a rhombus with diagonals 6 cm and 4 cm, what is the distance from the center to each vertex?
What is the measure of each interior angle of a regular hexagon?
In a trapezium ABCD where AD || BC, if BC = 8 cm and the construction requires drawing BE = 5 cm, what is the length of AD?
Sample Questions
Which of the following are required to construct a parallelogram? (Select all correct options)
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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.
Which construction methods can be used for a regular hexagon? (Select all correct)
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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.
What is the central angle subtended by each side of a regular hexagon at its center?
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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 or False: A square can be constructed using the same method as a rhombus construction.
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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.
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