Triangle Side Analysis: Determining if EB is a Valid Triangle Side

Given two triangles, Is EB a side of one of the triangles?

To determine if $EB$ is a side of either triangle, follow these steps:

• **Step 1:** Identify the vertices of the two triangles as shown in the diagram.
• **Step 2:** The first triangle has vertices $A$, $B$, and $C$. Hence, its sides are $AB$, $BC$, and $CA$.
• **Step 3:** The second triangle has vertices $D$, $E$, and $F$. Therefore, its sides are $DE$, $EF$, and $FD$.
• **Step 4:** Check if $EB$ is one of these sides.

On examining the sides listed for both triangles:

- For triangle $ABC$, we have sides $AB$, $BC$, and $CA$.

- For triangle $DEF$, we have sides $DE$, $EF$, and $FD$.

Clearly, $EB$ is not a side of either triangle.

Therefore, the solution to the problem is No, $EB$ is not a side of one of the triangles.