Triangle ABC Side Verification: Is AD a Valid Side?

Question

True or false:

AD is a side of triangle ABC.

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Video Solution

Solution Steps

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 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.

Answer

Not true