Triangle ABC Side Verification: Is AD a Valid Side?

Triangle Side Identification with Vertex Recognition

True or false:

AD is a side of triangle ABC.

AAABBBCCC

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Determine whether AD is a side in the given triangle
00:03 The line that connects the 2 points together is the side
00:06 This line connects A and B and therefore it is AB
00:09 The same thing for points A,C and B,C
00:19 Given that there is no point D in the triangle, AD cannot exist
00:22 This is the solution

Step-by-step written solution

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1

Understand the problem

True or false:

AD is a side of triangle ABC.

AAABBBCCC

2

Step-by-step solution

To determine if line segment AD is a side of triangle ABC, we need to agree on the definition of a triangle's side. A triangle consists of three sides, each connecting pairs of its vertices. In triangle ABC, these sides are AB, BC, and CA. Each side is composed of a direct line segment connecting the listed vertices.

In the diagram provided, there is no indication of a point D connected to point A or any other vertex of triangle ABC. To claim AD as a side, D would need to be one of the vertices B or C, or a commonly recognized point forming part of the triangle’s defined structure. The provided figure and description do not support that AD exists within the given triangle framework, as no point D is defined within or connecting any existing vertices.

Therefore, according to the problem's context and based on the definition of the sides of a triangle, AD cannot be considered a side of triangle ABC. It follows that the statement "AD is a side of triangle ABC" should be deemed not true.

3

Final Answer

Not true

Key Points to Remember

Essential concepts to master this topic
  • Triangle Definition: A triangle has exactly three sides connecting its vertices
  • Side Naming: Triangle ABC has sides AB, BC, and CA only
  • Verification: Check that both endpoints of the segment are vertices of the triangle ✓

Common Mistakes

Avoid these frequent errors
  • Assuming any line segment mentioned is a side of the triangle
    Don't assume AD is a side just because A is mentioned = incorrect identification! Point D is not shown or defined as a vertex of triangle ABC. Always verify that both endpoints of a segment are actual vertices of the given triangle.

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 segments are sides of a triangle?

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A triangle's sides connect its three vertices in pairs. For triangle ABC, the sides are AB, BC, and CA. Any other segment is not a side of this triangle.

What if there's a point D somewhere in the diagram?

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Even if point D exists, segment AD would only be a side if D replaced one of the original vertices (B or C). Since triangle ABC has vertices A, B, and C, AD cannot be a side.

Could AD be part of a different triangle?

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Yes! If points A and D are vertices of another triangle, then AD could be a side of that triangle. But the question asks specifically about triangle ABC.

How can I remember which segments are sides?

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Use the triangle's name as a guide! Triangle ABC has sides AB, BC, and CA. Each side uses exactly two of the three vertices in the name.

What's the difference between a side and other line segments?

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A side of a triangle connects two vertices and forms the boundary. Other segments like medians or altitudes might be inside the triangle, but they're not sides.

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