Question

Which of the following statements is/are correct?
We can construct a quadrilateral:
(A)When its opposite sides are given
(B)When its four angles and a side are given
(C)When its diagonals are given
(D) When its four sides and a diagonal are given

Answer 1

Hint: The word ‘Quad’ means four. So, a quadrilateral is a plane figure that has four sides or edges and also has four corners or vertices. Rectangle, square, parallelogram, trapezium, rhombus and kite etc. all are the types of quadrilateral having four sides. We must check each and every option and check which among them is/are true.

Complete step-by-step answer:
Consider a parallelogram $ABCD$.

Following are the properties of the parallelogram $ABCD$:-
(1)Four sides: $AB,BC,CD$ and $DA$
(2)Four vertices: Points $A,B,C$ and $D$
(3)Four angles: $\angle ABC,\angle BCD,\angle CDA$ and $\angle DAB$
(4) $\angle A$ and $\angle B$ are adjacent angles
(5) $\angle A$ and $\angle C$ are opposite angles
(6) $AB$ and $CD$ are opposite sides
(7) $AB$ and $AC$ are adjacent sides
(8) Sum of all four interior angles is $360^\circ $
Construction of a quadrilateral is possible only when-
When its four sides and one diagonal are given
When its three sides and two included angles are given
When its three angles and any two adjacent sides are given
When its four sides and a diagonal are given
When its three sides and two diagonals are given
When its four sides and an angle are given
So we have ‘when its four sides and a diagonal are given’ as an option.

Hence, option (D) is the correct answer.

Note: A quadrilateral has 8 elements- 4 sides and 4 angles. In addition to these elements a quadrilateral has 2 diagonals which play an important role in determining the size and shape of a quadrilateral.