Question

look at the diagram and evaluate. which of the statements below is false? answer pr > qr pq = qr ps > qr r is the midpoint of qs submit answer

Explanation:

Step1: Calculate lengths

$PQ = 7 - 2=5$; $QR = 13 - 7 = 6$; $PR=13 - 2 = 11$; $PS=19 - 2=17$; $QS = 19 - 7 = 12$.

Step2: Check first statement

$PR = 11$ and $QR = 6$, so $PR>QR$ is True.

Step3: Check second statement

$PQ = 5$ and $QR = 6$, so $PQ = QR$ is False.

Step4: Check third statement

$PS = 17$ and $QR = 6$, so $PS>QR$ is True.

Step5: Check fourth statement

Mid - point of $QS$ is $\frac{7 + 19}{2}=13$, which is the position of $R$, so “$R$ is the midpoint of $\overline{QS}$” is True.

Answer:

$PQ = QR$