Question

Diagonals of a Rectangle are ___________
A) equal
B) distinct
C) parallel
D) perpendicular

Answer 1

Hint: Here we are asked to find the property of a diagonal of a rectangle. For that, we need to construct a rectangle and list its properties. From that, we can get the property of a diagonal of a rectangle. The diagonals are drawn on closed figures having vertices or corners from one vertex to its opposite vertex.

Complete step by step answer:
We aim to find the property of a diagonal of a rectangle. Let us first construct a rectangle.
Draw a line segment \[AB\] with any measurement. Then draw two perpendicular lines from the point \[A\] and \[B\] with the same measurement (less than the line segment \[AB\]) and mark its ends as \[C\] and \[D\]. And finally, join the points \[C\] and \[D\].

Hence, we have constructed a rectangle $ABCD$. Now let us draw diagonals for this rectangle. The diagonals are drawn across the closed figures from a vertex to its opposite vertex diagonally. For the above rectangle, the diagonals will be \[AC\] and \[BD\].

Now let us see the properties of a rectangle. A rectangle is a 2-D figure having four sides. Its opposite sides are equal, that is \[AB = DC\] and \[AD = BC\]. Each interior angle in the rectangle is the right angle that is \[\angle A = \angle B = \angle C = \angle D = 90^\circ \]. The diagonals of a rectangle will intersect each other at the center of a rectangle. They bisect at different angles, acute and obtuse angles. Also, they are equal in length, that is \[AC = BD\].

Therefore, we can say that the diagonals of a Rectangle are equal. So, Option (A) is correct.

Note:
The \[2D\] figures are the figures having only two dimensions. A plane figure having at least three sides and angles is known as a polygon. A rectangle is nothing but a polygon of four sides. It is also known as a parallelogram with all the same angles. It is also a type of quadrilateral where all the angles are equal \[90^\circ \].