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

Q: How do I know which points belong to which triangle?

Look at the diagram carefully! Triangle $ ABC $ has vertices A, B, and C connected by lines. Triangle $ DEF $ has vertices D, E, and F connected by lines. Each triangle is a separate shape.

Q: Can two triangles share a side?

Yes, triangles can share sides when they have two vertices in common. But in this problem, the triangles are completely separate - they don't share any vertices.

Q: What are all the sides of triangle ABC?

Triangle ABC has three sides: $ AB $, $ BC $, and $ CA $. Remember, sides are named using the two vertices they connect!

Q: What are all the sides of triangle DEF?

Triangle DEF has three sides: $ DE $, $ EF $, and $ FD $. Notice that $ EB $ is not one of these sides.

Triangle Side Identification with Multiple Triangles

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

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

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

Step-by-step solution

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.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Triangle Sides: Each triangle has exactly three sides connecting vertices
Naming: Side $EB$ connects vertices E and B
Verification: Check if both vertices belong to same triangle ✓

Common Mistakes

Avoid these frequent errors

Assuming any two points form a triangle side
Don't connect any two points and call it a triangle side = wrong identification! Points E and B belong to different triangles, so EB is not a side of either triangle. Always check that both vertices belong to the same triangle.

Practice Quiz

Test your knowledge with interactive questions

True or false:

DE not a side in any of the triangles.

FAQ

Everything you need to know about this question

How do I know which points belong to which triangle?

Look at the diagram carefully! Triangle $ABC$ has vertices A, B, and C connected by lines. Triangle $DEF$ has vertices D, E, and F connected by lines. Each triangle is a separate shape.

Can two triangles share a side?

Yes, triangles can share sides when they have two vertices in common. But in this problem, the triangles are completely separate - they don't share any vertices.

What are all the sides of triangle ABC?

Triangle ABC has three sides: $AB$ , $BC$ , and $CA$ . Remember, sides are named using the two vertices they connect!

What are all the sides of triangle DEF?

Triangle DEF has three sides: $DE$ , $EF$ , and $FD$ . Notice that $EB$ is not one of these sides.

Why isn't EB a side if I can see both points E and B?

Just because you can see two points doesn't mean they form a triangle side! Triangle sides only connect vertices within the same triangle. Since E is in triangle DEF and B is in triangle ABC, EB is not a side of either triangle.

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