Ch 4 focuses on constructing quadrilaterals using compass and ruler. A quadrilateral has 10 elements (4 sides, 4 angles, 2 diagonals), but only 5 independent measurements are needed for a unique construction.
A unique quadrilateral can be constructed given: (1) 4 sides and 1 diagonal, (2) 2 diagonals and 3 sides, (3) 2 adjacent sides and 3 angles, (4) 3 sides and 2 included angles, (5) other special combinations.
General approach: draw the given side or diagonal as base, use compass for arcs of given lengths, use protractor for given angles, and identify the intersection points as vertices.
Download: https://ncert.nic.in/textbook/pdf/hemh104.pdf | Complete book: https://ncert.nic.in/textbook/pdf/hemh1ps.zip
A quadrilateral has 5 degrees of freedom. With fewer than 5 measurements, multiple quadrilaterals are possible. With 5 independent measurements, the quadrilateral is uniquely determined.
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