Triangle Side Analysis: Is AC a Side of Triangle BDC?

Triangle Side Identification with Non-Vertex Points

True or false:

AC is a side of triangle BDC.

AAABBBCCCDDD

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Determine whether AC is a side in the given triangle BDC
00:03 Identify the sides of triangle BDC
00:07 Mark the side with the two letters at the beginning/end of the line
00:11 These are the sides of triangle BDC
00:14 Therefore, we can observe that AC is not part of triangle BDC
00:17 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

True or false:

AC is a side of triangle BDC.

AAABBBCCCDDD

2

Step-by-step solution

To determine whether AC is a side of triangle BDC, let us take the following steps:

  • Identify the vertices of triangle BDC, which are points B, D, and C.
  • Consider the sides of triangle BDC which are BD, DC, and BC, as each side is formed by connecting two vertices of the triangle.

Analysis:

Triangle BDC has exactly three sides, formed by the segments connecting vertices B, D, and C, which are:

  • BD (connecting vertices B and D)
  • DC (connecting vertices D and C)
  • BC (connecting vertices B and C)

Since segment AC does not connect any two vertices of triangle BDC, it cannot be a side of this triangle.

Thus, the statement "AC is a side of triangle BDC" is False.

Therefore, the solution to the problem is False.

3

Final Answer

False

Key Points to Remember

Essential concepts to master this topic
  • Definition: Triangle sides connect only the three vertices of that triangle
  • Method: List triangle BDC vertices as B, D, C; sides are BD, DC, BC
  • Check: AC connects A and C, but A is not a vertex of triangle BDC ✓

Common Mistakes

Avoid these frequent errors
  • Assuming any line segment in the diagram is a side
    Don't think every line segment shown is automatically a side of every triangle = wrong identification! Just because AC exists in the diagram doesn't make it part of triangle BDC. Always identify the specific triangle's three vertices first, then determine which segments connect those vertices.

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 points are vertices of a specific triangle?

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Look at the triangle name! Triangle BDC has vertices B, D, and C. The letters in the name tell you exactly which three points form that triangle.

Can a line segment be part of multiple triangles?

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Yes! For example, if you have triangles ABC and BCD, then segment BC would be a side of both triangles since it connects vertices in each triangle.

What if I see more than three points in the diagram?

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That's normal! Diagrams often show multiple points and triangles. Focus only on the specific triangle mentioned in the question and ignore extra points that aren't its vertices.

Does the order of vertices in the triangle name matter?

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No! Triangle BDC is the same as triangle DCB or triangle CBD. The three letters identify the vertices regardless of order, and the sides are always the segments connecting these three points.

How can I double-check my answer?

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List the triangle's three vertices, then write all possible sides (there are exactly 3). If your segment connects two of these vertices, it's a side. If not, it isn't!

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