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

The triangle ABC is shown below.

To which side(s) are the median and the altitude drawn?

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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