Triangle Side Verification: Is BD a Side of Triangle BCD?

Triangle Naming with Vertex Identification

True or false:

BD is a side of triangle BCD.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Determine whether BD is a side in the given triangle BCD
00:03 Identify the sides of the triangle BCD
00:06 Each combination of two letters represents a side in the triangle
00:10 Proceed to examine all of the potential combinations in order to identify all of the sides (There are a total of 3 sides)
00:16 Therefore, we can observe that BD is part of triangle BCD
00:20 This is the solution

Step-by-step written solution

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1

Understand the problem

True or false:

BD is a side of triangle BCD.

2

Step-by-step solution

To ascertain whether BD is a side of triangle BCD, observe the basic geometric principles associated with triangles.

In Euclidean geometry, a triangle is named based on its vertices. For triangle BCD, it consists of three vertices: B, C, and D.

The sides of the triangle are the line segments directly joining these vertices. Thus, the sides of triangle BCD are:

  • Line segment BC, connecting vertices B and C.
  • Line segment CD, connecting vertices C and D.
  • Line segment BD, connecting vertices B and D.

Line segments such as BD connect two vertices within the triangle and thus qualify as one of its sides. This aligns with the standard definition of a triangle in Euclidean geometry, where any side is formed by connecting two of its vertices.

Therefore, indeed, BD is a side of triangle BCD.

The correct conclusion is true: BD is a side of triangle BCD.

3

Final Answer

True

Key Points to Remember

Essential concepts to master this topic
  • Triangle Sides: Connect any two vertices of the triangle
  • Technique: Triangle BCD has sides BC, CD, and BD
  • Check: Count vertices B, C, D - any pair forms a side ✓

Common Mistakes

Avoid these frequent errors
  • Confusing sides with other geometric elements
    Don't think BD might be a diagonal or height = wrong classification! BD connects two vertices of triangle BCD, making it a legitimate side by definition. Always remember that triangle sides are simply line segments connecting any two vertices.

Practice Quiz

Test your knowledge with interactive questions

Is DE side in one of the triangles?
AAABBBCCCDDDEEE

FAQ

Everything you need to know about this question

How do I know which line segments are sides of a triangle?

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A triangle's sides are the line segments that connect its vertices. For triangle BCD, the vertices are B, C, and D, so the sides are BC, CD, and BD - that's it!

Can a triangle have more than 3 sides?

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No! By definition, a triangle always has exactly 3 sides and 3 vertices. If it had more sides, it would be a different polygon like a quadrilateral or pentagon.

What's the difference between a side and a diagonal in triangles?

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In triangles, there are no diagonals! Every line segment connecting two vertices is a side. Diagonals only exist in polygons with 4 or more sides.

Does the order of vertices in the triangle name matter?

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Not for identifying sides! Triangle BCD, triangle CBD, and triangle DBC all have the same three sides: BC, CD, and BD. The order might matter for other properties, but not for basic side identification.

How can I be sure BD is really a side and not something else?

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Ask yourself: Does BD connect two vertices of the triangle? Since B and D are both vertices of triangle BCD, BD is definitely a side. It's that simple!

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