Question

Given that PQ=QR=RS=SP, identify the additional information needed to conclude that PQRS is a square.

Answer 1

To conclude that PQRS is a square, we need additional information confirming that all internal angles are right angles or that it is both a rectangle and a rhombus.

Step-by-step explanation:

To determine that a quadrilateral PQRS is a square, knowing that PQ=QR=RS=SP is not enough. In addition to equal sides, we need information on the angles of the quadrilateral. Specifically, we need to know that all internal angles are right angles (90 degrees). Alternatively, knowing that the quadrilateral is both a rectangle (which has equal angles) and a rhombus (which has equal sides) would suffice, since a square is essentially a rectangle with equal sides.

Answer 2

Option 3

Step-by-step explanation:

With all sides equal all angles have to be 90° for a quadrilateral to be a square.

When all angles are 90, then the diagonal would be equal in length

A rhombus also has all sides equal in length, but the diagonals are not equal in length because the angles are not all 90