We will examine whether the given information in the diagram is enough to classify the below quadrilateral as a square.
To do so, we will first consider the Square Corollary (Corollary 7.4).
Square Corollary
A quadrilateral is a square if and only if it is a rhombus and a rectangle.
By this corollary, for JKLM to be a square it needs to have the properties of both rhombuses and rectangles. Let's recall these properties.
Properties of a Rhombus:
A quadrilateral is a rhombus if and only if its four sides are congruent.
A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles.
A parallelogram is a rhombus if and only if its diagonals are perpendicular.
Properties of a Rectangle:
A quadrilateral is a rectangle if and only if it has four right angles.
A parallelogram is a rectangle if and only if its diagonals are congruent.
The quadrilateral in the diagram provides the properties of a rectangle. However, it satisfies none of the properties of a rhombus. Thus, it might be a rectangle rather than a square. Consequently, we can conclude that there is not enough information to classify the quadrilateral as square.
