Question

analyze consider rectangle qrst with qr = st = 4 centimeters and rs = qt = 2 centimeters. if point u is on $overline{qr}$ such that qu = ur and point v is on $overline{rs}$ such that rv = vs, then is $overline{qu}$ congruent to $overline{rv}$? justify your argument.

Explanation:

Step1: Calculate the length of $\overline{QU}$

Since $QR = 4$ cm and $QU=UR$, then $QU=\frac{QR}{2}=\frac{4}{2} = 2$ cm.

Step2: Calculate the length of $\overline{RV}$

Since $RS = 2$ cm and $RV = VS$, then $RV=\frac{RS}{2}=\frac{2}{2}=1$ cm.

Step3: Compare the lengths

Since $QU = 2$ cm and $RV=1$ cm, $QU
eq RV$. In geometry, two line - segments are congruent if and only if they have the same length. So, $\overline{QU}$ is not congruent to $\overline{RV}$.

Answer:

$\overline{QU}$ is not congruent to $\overline{RV}$ because $QU = 2$ cm and $RV = 1$ cm and congruent line - segments have equal lengths.