Question

is parallelogram pqrs a rhombus? yes no

Explanation:

Step1: Use the property of parallelogram

In a parallelogram \(PQRS\), \(PS\parallel QR\) and \(PQ\parallel SR\). So, \(\angle PSQ=\angle RQS\) (alternate - interior angles) and \(\angle PQS = \angle RSQ\) (alternate - interior angles).

Step2: Check the condition for a rhombus

One of the properties of a rhombus is that the diagonals bisect the vertex angles. In a parallelogram, if the diagonals bisect the vertex angles, then it is a rhombus.
Here, \(\angle PSR=\angle PSQ+\angle RSQ=53^{\circ}+ 52^{\circ}=105^{\circ}\)
If \(SQ\) were a diagonal that bisects \(\angle PSR\) in a rhombus, the two angles formed by the diagonal \(SQ\) with \(\angle PSR\) would be equal. But \(53^{\circ}
eq52^{\circ}\)

Answer:

no