Triangle Side Identification: Is CB a Valid Side in Given Triangles?

Triangle Side Identification with Vertex Labels

Look at the two triangles below.

Is CB a side of one of the triangles?

AAABBBCCCDDDEEEFFF

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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 CB a side of one of the triangles?

AAABBBCCCDDDEEEFFF

2

Step-by-step solution

In order to determine if segment CB is a side of one of the triangles, let's start by identifying the triangles and their corresponding vertices from the given diagram:

  • Triangle 1 has vertices labeled as A, B, C.
  • Triangle 2 has vertices labeled as D, E, F.

Now, to decide if CB is a side, we need to check if a line segment exists between points C and B in any of these triangles.

Upon examining the points:

  • Point C is present in triangle 1.
  • Point B is also present in triangle 1.
  • The line segment connecting B and C is visible, forming the base of triangle 1.

Therefore, segment CB is indeed a side of triangle ABC, confirming that the answer is Yes.

Thus, the solution to the problem is Yes \text{Yes} .

3

Final Answer

Yes.

Key Points to Remember

Essential concepts to master this topic
  • Definition: A side connects two vertices that belong to the same triangle
  • Technique: Check if both points C and B exist in triangle ABC
  • Verification: Trace the line segment CB in the diagram visually ✓

Common Mistakes

Avoid these frequent errors
  • Confusing vertex order with side existence
    Don't assume CB doesn't exist just because you see BC written differently = missing valid sides! The order of letters doesn't matter for naming sides. Always check if both vertices belong to the same triangle regardless of letter order.

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

Does it matter if I write CB or BC?

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No, it doesn't matter! Both CB and BC refer to the same line segment connecting points C and B. In geometry, the order of letters when naming a side is not important.

How do I know which points belong to which triangle?

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Look at the vertex labels in the diagram. Triangle 1 has vertices A, B, C, while Triangle 2 has vertices D, E, F. Each triangle's sides connect only its own vertices.

What if the triangles share a vertex?

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If triangles share a vertex, that point can be part of multiple triangles. However, a side only exists if both endpoints belong to the same triangle.

Can I just look at the diagram to find the answer?

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Yes! Visual inspection is a valid method here. Look for a line segment connecting the two points in question. If you can trace it, then it's a side of that triangle.

What makes something a 'side' of a triangle?

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A side is a line segment that connects two vertices of the same triangle. Every triangle has exactly three sides connecting its three vertices.

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