Question

what is the minimum number of measurements required to construct a unique quadrilateral, square, rectangle, rhombus, parallelogram.

Answer 1

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Five measurements

Five measurements can determine a quadrilateral uniquely. A quadrilateral can be constructed uniquely if the lengths of its four sides and a diagonal are given. A quadrilateral can be constructed uniquely if the lengths of its three sides and two diagonals are given.

Answer 2

The minimum number of measurements required to construct a unique quadrilateral, square, rectangle, rhombus, or parallelogram are five, one, two, two, and three respectively.

• To construct a quadrilateral minimum of one base length, two angles made by the base and two lengths to the angles made by the base are required.
• In a square, all the sides the equal and measure of all the angles is 90°.
• In a rectangle the opposite two sides are equal and all the angles are 90°.
• All sides of a rhombus are equal while constricting a rhombus we need to know the angle and all the angles are not equal.
• In a parallelogram the opposite sides and opposite angles are equal. So to construct a parallelogram we need to have the measurements of the two adjacent sides of the parallelogram and the angle between them.

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