Choose given statement is true or false:

A rectangle is a convex quadrilateral because both of its diagonals lie at its exterior.

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True

False

answer is B.

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Detailed Solution

The given statement is false.
Concept: A rectangle is indeed a two-dimensional (2D) shape with opposite sides that are parallel and equal to each other and four right angles. A four-sided polygon with inner angles that are less than 180 degrees each is referred to as a convex quadrilateral. These quadrilaterals completely encompass the diagonals.
The convex quadrilateral has the characteristic that its diagonals are internal to the quadrilateral. The diagonals of the rectangle must therefore be inside the rectangle if it is a convex quadrilateral. Based on their sides and angles, convex quadrilaterals may be divided into various subcategories.
A rectangle has four sides, each of which is equal and parallel to the other.
Each angle

.
If we connect the opposite corners, the diagonals would be entirely within the rectangle's interior.
Additionally, all the angles are less than

.
The given statement, therefore becomes untrue and the correct statement would be, that a rectangle is a convex quadrilateral as it has its diagonal interior to the quadrilateral and not exterior.
Hence, the given statement is false.

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