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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Important Questions from Quadrilaterals
What is the value of AC 2– BD 2
What is the point of intersection of the diagonals?
What is the area of the parallelogram?
ABCD is a cyclic quadrilateral. Diagonals BD and AC intersect each other at E. If ∠BEC = 138° and ∠ECD = 35°, then what is the measure of ∠BAC?
A circle is inscribed in a quadrilateral ABCD, touching sides AB, BC CD and DA at P, Q, R and S, respectively. If AS = 6 cm, BC = 12 cm, and CR = 5 cm, then the length of AB (in cm) is:
