Question

State with reason whether the following statement is ‘true’ or ‘false’.
Every rhombus is a rectangle.

Answer 1

Hint: Quadrilateral is the closed figure which has the four sides and the four vertices. Quadrilateral is also known as a “quadrangle”. Fundamentally, there are six types of quadrilaterals such as rectangle, square, kite, rhombus, trapezium and parallelogram. Referring the properties of rhombus and rectangle will justify and find out whether the given statement is true or false.

Complete step-by-step answer:
Rhombus – Rhombus can be defined as the closed figure with all the four sides equal and opposite two sides of the rhombus are parallel to each other and the diagonals of the rhombus always intersect at right angles.

Rectangle- Rectangle can be defined as the closed figure with opposite two sides of the quadrilateral are equal and parallel to each other.

Hence, every rhombus is not a rectangle since the rectangle makes ninety angles of measure with its adjacent side but the rhombus does not make ninety degrees with the adjacent sides.

Note: Follow the properties of the parallelogram properly. Always remember that the opposite two sides of the parallelogram are always equal. Remember all rhombuses are parallelograms, but not all the parallelograms are rhombuses.