Geometry Problem: Is Line Segment DE Part of the Triangle?

Triangle Side Identification with Line Segments

Is DE side in one of the triangles?
AAABBBCCCDDDEEE

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1

Understand the problem

Is DE side in one of the triangles?
AAABBBCCCDDDEEE

2

Step-by-step solution

Since line segment DE does not correspond to a full side of any of the triangles present within the given geometry, we conclude that the statement “DE is a side in one of the triangles” is Not true.

3

Final Answer

Not true

Key Points to Remember

Essential concepts to master this topic
  • Definition: Triangle sides connect two vertices of the same triangle
  • Technique: Check if line segment connects vertices A-B, B-C, or A-C
  • Verification: Count all triangles present and list their three sides each ✓

Common Mistakes

Avoid these frequent errors
  • Assuming all line segments are triangle sides
    Don't think every line segment in a figure is automatically a side of a triangle = wrong identification! Line segments can be diagonals, altitudes, or other geometric elements. Always check if the segment connects two vertices that form a complete triangle.

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 identify what triangles are in this figure?

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Look for three points connected by three line segments that form a closed shape. In this figure, triangle ABC is formed by connecting points A, B, and C.

What makes DE different from the triangle sides?

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DE is a line segment inside the triangle, but it doesn't connect two vertices of triangle ABC. The actual sides are AB, BC, and AC.

Can a line segment be part of multiple triangles?

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Yes! If triangles share vertices, they can share sides too. But in this case, DE doesn't form a side of any triangle in the figure.

How do I know if I've found all the triangles?

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Count systematically: look for every possible combination of three points that are connected by line segments. Make sure each set of three points forms a complete closed triangle.

What if there are more than three points in the figure?

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More points can create multiple triangles! Always check each possible triangle separately and identify its three sides before determining if your line segment belongs to any of them.

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