Question

question
which segment is opposite to ∠r?

answer
ra rh ah

Explanation:

Step1: Recall triangle opposite side rule

In a triangle, the side opposite an angle is the side that does not form the angle. For $\angle R$, the angle is at vertex $R$. The sides forming $\angle R$ are $RA$ and $RB$ (wait, in the triangle with vertices $R$, $A$, $H$, $\angle R$ is at $R$, so the sides adjacent to $\angle R$ are $RB$ (wait, labels: vertices are $R$, $A$, $H$, right angle at $A$. So $\angle R$ is at $R$, between sides $RA$ and $RH$? Wait no, the triangle has vertices $R$, $A$, $H$, with right angle at $A$. So sides: $RA$, $AH$, $RH$. $\angle R$ is at $R$, so the sides meeting at $R$ are $RH$ and $RA$? Wait no, vertex $R$ is connected to $H$ and $A$. So $\angle R$ is between $RH$ and $RA$? Wait, no, the triangle is $R - A - H$, right-angled at $A$. So sides: $RA$ (from $R$ to $A$), $AH$ (from $A$ to $H$), $RH$ (from $R$ to $H$). The angle at $R$ ($\angle R$) is formed by sides $RA$ and $RH$? Wait, no, the two sides forming $\angle R$ are $RR$? No, vertices are $R$, $A$, $H$. So $\angle R$ is between $R$ to $A$ (side $RA$) and $R$ to $H$ (side $RH$). Therefore, the side opposite $\angle R$ is the side that is not connected to $R$, which is $AH$. Wait, the options are $RA$, $RH$, $AH$ (wait the options are $RA$, $RH$, $AH$? Wait the user's options: $RA$, $RH$, $AH$ (written as $AH$? Wait the third option is $AH$? Wait the original options: first is $RA$, second $RH$, third $AH$ (maybe labeled as $AH$ with $A$ and $H$). So in triangle $RAH$ (right-angled at $A$), $\angle R$ is at $R$. The side opposite $\angle R$ is the side that does not have vertex $R$, so it's $AH$. Let's check: angle at $R$: the sides adjacent are $RA$ (from $R$ to $A$) and $RH$ (from $R$ to $H$). So the opposite side is $AH$. So among the options, the third option is $AH$ (labeled as $AH$? Wait the third option is $\overline{AH}$? So the answer is $AH$.

Step2: Confirm with triangle side-angle opposite definition

In a triangle, the side opposite an angle is the side that is across from the angle, i.e., it does not share the angle's vertex. For $\angle R$ (vertex $R$), the side opposite is the one with vertices $A$ and $H$, which is $AH$. So the correct option is the third one, $AH$.

Answer:

$\overline{AH}$ (or the third option, labeled as $AH$ in the options)