Question

is parallelogram rstu a rhombus? yes no

Explanation:

Step1: Recall the property of a rhombus

A rhombus is a parallelogram with diagonals that bisect the angles.

Step2: Check the angle - bisecting property

In parallelogram \(RSTU\), if \(TR\) is a diagonal, for it to be a rhombus, \(\angle UTR\) should be equal to \(\angle STR\) and \(\angle URT\) should be equal to \(\angle SRT\).
We know that in a parallelogram \(UT\parallel SR\), so \(\angle UTR=\angle SRT = 54^{\circ}\) (alternate - interior angles) and \(\angle URT=\angle STR=56^{\circ}\) (alternate - interior angles). Since the diagonal \(TR\) does not bisect the angles \(\angle UTS\) and \(\angle URS\) (because \(54^{\circ}
eq56^{\circ}\)), the parallelogram \(RSTU\) is not a rhombus.

Answer:

no