Do This: 8 cm D A 6 cm 6 cm B 8 cm 8 cm D 6 cm . B 8 cm (i) 8 cm D А 6 cm Take a pair of sticks of equal length, say 8 cm. Take another pair of sticks of equal length, say, 6 cm. Arrange them suitably to get a rectangle of length 8 cm and breadth 6 cm. This rectangle is created with the 4 available measurements. Now just push along the breadth of the (1) rectangle. Does it still look alike? You will get a new shape of a rectangle Fig (ii), observe that the rectangle has now become a parallelogram. Have you altered the lengths of the sticks? No! The measurements of sides 6cm remain the same. Give another push to the newly obtained shape in the opposite direction; what do you get? You again get a parallelogram again, which is altogether different Fig (iii). Yet the four measurements remain the same. This shows that 4 measurements of a quadrilateral cannot determine its uniqueness. So, how 6 cm many measurements determine a unique quadrilateral? Let us go back to the activity! You have constructed a rectangle with two sticks each of length 8 cm and other two sticks each of length 6 cm. Now introduce another stick of length equal to BD and put it along BD (Fig iv). If you push the breadth now, does the shape change? No! It cannot, without making the figure open. The introduction of the fifth stick has (iv) fixed the rectangle uniquely, i.e., there is no other quadrilateral (with the given lengths of sides) possible now. Thus, we observe that five measurements can determine a quadrilateral uniquely. But will any five measurements (ofsides and angles) be sufficient to draw a unique quadrilateral? B 8 cm 8 cm 6 cm 6 cm B с 8 cm
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YES ANY 5 INDIVIDUAL MEASUREMENTS ARE NEEDED TO CONSTRUCT A QUADIILATERAL
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