Which of the following are true to construct a quadrilateral uniquely? (i) Rhombus and square can be constructed when 2 diagonals are given. (ii) The lengths of 2 adjacent sides and 2 angles are given. (iii) The lengths of 3 sides and 1 angle are given. (iv) The lengths of 4 sides and 1 diagonal are given.
(i) and (iv)
A rhombus or square is fully determined by its two diagonals, since they are perpendicular bisectors that fix all four vertices uniquely — statement (i) is true.
Four sides and one diagonal split the quadrilateral into two triangles, each constructible by SSS, uniquely fixing the shape — statement (iv) is true.
Two adjacent sides and two angles, or three sides and one angle, do not provide enough independent constraints to fix a general quadrilateral uniquely.
Hence, statements (i) and (iv) are the correct combination for unique construction.
Similar Questions
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- In a rhombus ABCD, if $\angle ACB = 40^\circ, \text{then } \angle ADB = ?$
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If AD = 10 cm, then CD = ?
Important Questions from Quadrilaterals
The ratio between the length and breadth of a rectangular park is 3 : 2. If a man cycling along the boundary at the speed of 12 km per hour completes one round in 8 minutes, then the area of the park in square meter will be
A quadrilateral whose four sides and angles are equal to each other is known as
The sides of a quadrilateral are in the ratio of 3 ∶ 4 ∶ 6 ∶ 8. If the perimeter of the quadrilateral is 84 cm. Find the longest side of the quadrilateral.
The side of a rhombus is 26 cm. The length of one of its diagonals is 20 cm. The sum of the lengths of the diagonals of this rhombus is equal to the perimeter of a rectangle. If the difference between the length and breadth of the rectangle is 6 cm, then what is the area of the rectangle?
PQRS is a cyclic quadrilateral. If ∠P is 4 times ∠R, and ∠S is 3 times ∠Q, then the average of ∠Q and ∠R is:
