Question

To construct a convex quadrilateral, which of the following cases is not correct?
Option A: when the lengths of four sides and one diagonal are given.
Option B: when the lengths of three sides and two diagonals are given.
Option C: when the lengths of four sides and one angle are given.
Option D: when the lengths of two sides and two included angles are given.

Answer 1

Hint: A quadrilateral is a 4-sided polygon. There are two types of quadrilaterals-convex and concave. A concave quadrilateral can be categorized by two things-when all the diagonals are inside the quadrilateral and atleast one of the interior angles is greater than 180°. A convex quadrilateral can be categorized by two things, all the diagonals are inside the figure and all the interior angles are less than 180°.

The first figure is a convex quadrilateral. The second figure is concave quadrilateral.


Complete step-by-step answer:
When we want to construct any figure, there will be a few required measurements.
For example: To construct a right-angled triangle, we need the length of hypotenuse and another side.
To construct a convex quadrilateral, we need atleast 5 measurements, of either the angles or sides or diagonals.
The four options given are:
Option A: when the lengths of four sides and one diagonal are given.
In this, we have 5 measurements. Hence, this is a correct option.
Option B: when the lengths of three sides and two diagonals are given.
In this, we have 5 measurements. Hence this option is also correct.
Option C: when the lengths of four sides and one angle are given.
In this, we have measurements. This is also a correct option.
Option D: when the lengths of two sides and two included angles are given.
In this, we are given only four measurements. We can not construct a quadrilateral with 4 measurements. This is the incorrect option.

So, the correct answer is “Option D”.

Note: To construct a quadrilateral, we require 5 measurements which can be of either sides, angles of diagonals. It is possible to construct a convex quadrilateral, options A, B and C are enough but option D would not be enough. We can answer this question by also trying to draw a rough figure by giving information in all four options.