Question

Explain why a rectangle is a convex quadrilateral.
 Answer is Both of its diagonals lie at its exterior.
(a)True.
(b)False.

Answer 1

Hint: For a figure to be convex quadrilateral, the diagonals must lie interior to the quadrilateral. So, the statement of answer given in the question is straight forward..


Complete step-by-step answer:
Let us check whether the explanation given in the question about rectangles being a convex quadrilateral is true or false.
There is a property of the convex quadrilateral that its diagonals lie interior to the quadrilateral. So, if the rectangle is a convex quadrilateral, the diagonals of the rectangle must lie inside the rectangle.
The properties of rectangle are as follows:
Opposite angles are equal in the rectangle.
All the angles of the rectangle are of 90°.
Opposite sides of the rectangle are equal.
If we make a diagonal from any corner of the rectangle to the opposite corner, it will completely lie inside the rectangle.
All the angles are less than 180°.

As we have seen from the above figure and the properties of the rectangle, that both the diagonals lie interior to the rectangle.
Now, the statement of the explanation given in the question is saying that “Both of its diagonals lie at its exterior” which is false because as we have proved above that the diagonals of the rectangle lie completely interior to the rectangle.
Hence, the answer to the above question is false.

Note: If we don’t know what a convex quadrilateral is, we can still answer this question because we know the basic properties of the rectangle including that the diagonals lie interior to the rectangle which itself will falsify the explanation given in the question.