Question

what additional information is needed to prove that the triangles are similar? to prove △xyz ~ △mno using sss, you need to know that. now that y z, you need to know that angle to prove △xyz ~ △mno. options: mn = 6 and xz = 6; mn = 6 and xz = 17.5; mn = 17.5 and xz = 6

Explanation:

Step1: Recall SSS Similarity

SSS similarity requires corresponding sides to be proportional. For $\triangle XYZ$ and $\triangle MNO$, sides $YZ = 14$, $NO = 4$; $XY = 21$, $MN =?$; $XZ =?$, $MO = 5$.

Step2: Find Proportion

Ratio of $YZ$ to $NO$ is $\frac{14}{4}=\frac{7}{2}$. So other sides should have the same ratio. For $XY = 21$, $MN$ should satisfy $\frac{21}{MN}=\frac{7}{2}\implies MN = 6$. For $MO = 5$, $XZ$ should satisfy $\frac{XZ}{5}=\frac{7}{2}\implies XZ = 17.5$.

Step3: Check Options

Option "MN = 6 and XZ = 17.5" matches the proportional sides for SSS similarity.

Answer:

MN = 6 and XZ = 17.5