Triangle Side Identification: Is BC a Side in the Given Triangles?

Q: What's the difference between a side and a vertex?

A vertex is a corner point (like A, B, C), while a side is a line segment connecting two vertices (like $ AB $, $ BC $, $ CA $).

Q: Do I need to write sides in a specific order?

No! Side $ BC $ is the same as side $ CB $ - they both represent the line segment connecting vertices B and C.

Q: How many sides does each triangle have?

Every triangle has exactly 3 sides. Triangle ABC has sides $ AB $, $ BC $, and $ CA $. Triangle DEF has sides $ DE $, $ EF $, and $ FD $.

Triangle Vertex Naming with Side Identification

Look at the two triangles below.

Is BC 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

Look at the two triangles below.

Is BC a side of one of the triangles?

Step-by-step solution

Let's solve the problem step-by-step.

We first consider the two triangles given in the diagram. The vertices of the first triangle are labeled $A$ , $B$ , and $C$ . The vertices of the second triangle are labeled $D$ , $E$ , and $F$ .
Identify the sides of the first triangle: Since the vertices are $A$ , $B$ , and $C$ , the sides of the triangle are $AB$ , $BC$ , and $CA$ .
Identify the sides of the second triangle: With vertices $D$ , $E$ , and $F$ , the sides are $DE$ , $EF$ , and $FD$ .
Now, we ascertain whether $BC$ is a side. Upon inspection, $BC$ is clearly the side connecting vertex $B$ and vertex $C$ in the first triangle.

Thus, we conclude that Yes, $BC$ is indeed a side of one of the triangles.

The solution to the problem is: Yes

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic

Side Definition: Triangle sides connect two adjacent vertices directly
Technique: List all vertices first: Triangle ABC has sides AB, BC, CA
Check: Verify both letters appear as vertices in same triangle ✓

Common Mistakes

Avoid these frequent errors

Assuming letters represent sides without checking vertices
Don't assume BC is a side just because you see letters B and C = wrong identification! You might be looking at vertices from different triangles. Always verify both letters are vertices of the same triangle first.

Practice Quiz

Test your knowledge with interactive questions

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 letters represent the vertices of each triangle?

Look carefully at the diagram! Each vertex is marked with a dot and labeled with a letter. Triangle 1 has vertices A, B, C, while Triangle 2 has vertices D, E, F.

What's the difference between a side and a vertex?

A vertex is a corner point (like A, B, C), while a side is a line segment connecting two vertices (like $AB$ , $BC$ , $CA$ ).

Do I need to write sides in a specific order?

No! Side $BC$ is the same as side $CB$ - they both represent the line segment connecting vertices B and C.

How many sides does each triangle have?

Every triangle has exactly 3 sides. Triangle ABC has sides $AB$ , $BC$ , and $CA$ . Triangle DEF has sides $DE$ , $EF$ , and $FD$ .

Can two different triangles share the same side?

Only if they share vertices! In this problem, the triangles have completely different vertices (ABC vs DEF), so they cannot share any sides.

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