Triangle Side Identification: Determining if EC is a Valid Triangle Side

Triangle Naming with Vertex Identification

Look at the two triangles below. Is EC a side of one of the triangles?

AAABBBCCCDDDEEEFFF

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Let's see if E C is a side in one of the triangles.
00:09 First, check the sides of triangle A B C.
00:14 Write down all the sides of triangle A B C.
00:18 E C is not a side in triangle A B C. Let's look at triangle D E F.
00:24 Now, list all the sides of triangle D E F.
00:31 E C is not a side here either.
00:37 And that's our solution! E C is not a side in either triangle.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Look at the two triangles below. Is EC a side of one of the triangles?

AAABBBCCCDDDEEEFFF

2

Step-by-step solution

Every triangle has 3 sides. First let's go over the triangle on the left side:

Its sides are: AB, BC, and CA.

This means that in this triangle, side EC does not exist.

Let's then look at the triangle on the right side:

Its sides are: ED, EF, and FD.

This means that in this triangle, side EC also does not exist.

Therefore, EC is not a side in either of the triangles.

3

Final Answer

No

Key Points to Remember

Essential concepts to master this topic
  • Triangle Definition: Three vertices connected by exactly three sides
  • Naming Convention: Sides use two consecutive vertices like AB, BC, CA
  • Verification: Check if both letters appear as vertices in same triangle ✓

Common Mistakes

Avoid these frequent errors
  • Assuming any two letters form a valid side
    Don't connect any two vertices from different triangles = invalid side! Points E and C are in different triangles and not directly connected. Always check that both vertices belong to the same triangle before naming a side.

Practice Quiz

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Is the straight line in the figure the height of the triangle?

FAQ

Everything you need to know about this question

How do I know which vertices belong to the same triangle?

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Look at the connecting lines in the diagram. Vertices are only connected if there's a direct line between them. In this problem, triangle ABC has vertices A, B, C connected, while triangle DEF has vertices D, E, F connected.

Can I name a side using any two letters?

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No! A side must connect two vertices that are directly linked in the same triangle. You can't create sides between vertices from different triangles.

What if the vertices look close together?

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Distance doesn't matter - only actual connections do! Even if two points appear close, they only form a side if there's a line drawn between them in the same triangle.

How many sides does each triangle have?

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Every triangle has exactly 3 sides, no more, no less. Triangle ABC has sides AB, BC, and CA. Triangle DEF has sides DE, EF, and FD.

Why isn't EC a valid side?

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Because E belongs to triangle DEF and C belongs to triangle ABC. Since they're in different triangles, there's no direct connection between them, so EC cannot be a side.

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