Identify Segment DE: Analyzing Triangle Side Relationships

Q: How do I know which points are vertices of which triangle?

Look at the triangle shapes in the diagram. Each triangle has exactly three vertices - the corner points where two sides meet. Triangle ABC has vertices A, B, and C, while triangle DEF has vertices D, E, and F.

Q: What if two points are close together but in different triangles?

Being close doesn't matter! A side only exists if both points are vertices of the same triangle. For example, even if C and D were near each other, CD wouldn't be a side because C belongs to triangle ABC and D belongs to triangle DEF.

Q: How many sides does each triangle have?

Every triangle has exactly three sides. Triangle ABC has sides AB, BC, and AC. Triangle DEF has sides DE, EF, and DF. That's it - no more, no less!

Q: Can I just look at the diagram to see the sides?

Yes! The sides are the line segments you can see drawn between vertices. But always double-check by naming - if you can see a line connecting two vertices of the same triangle, that's a side.

Triangle Sides with Vertex Identification

Look at the two triangles below. Is DE a side of one of the triangles?

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at the two triangles below. Is DE a side of one of the triangles?

Step-by-step solution

To solve whether the segment $DE$ is a side of one of the triangles, we must identify the sides of each triangle in the given diagram.

The first triangle is labeled $\triangle ABC$ :

Vertices are $A, B,$ and $C$ .
Sides by this configuration are $AB, BC,$ and $AC$ .

The second triangle is labeled $\triangle DEF$ :

Vertices are $D, E,$ and $F$ .
Sides formed are $DE, EF,$ and $DF$ .

Upon inspection, we see that $DE$ is listed as a side of $\triangle DEF$ , confirming that it indeed is one side of this triangle.

Therefore, the conclusion is:

Yes, $DE$ is a side of one of the triangles.

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic

Rule: A triangle side connects exactly two vertices of the triangle
Technique: List vertices first: Triangle ABC has sides AB, BC, AC
Check: Verify both letters appear as vertices in the same triangle ✓

Common Mistakes

Avoid these frequent errors

Assuming any two labeled points form a triangle side
Don't assume DE is a side just because D and E are labeled points = wrong triangle identification! Points must be vertices of the same triangle to form a side. Always check which triangle contains both vertices as corners.

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 know which points are vertices of which triangle?

Look at the triangle shapes in the diagram. Each triangle has exactly three vertices - the corner points where two sides meet. Triangle ABC has vertices A, B, and C, while triangle DEF has vertices D, E, and F.

What if two points are close together but in different triangles?

Being close doesn't matter! A side only exists if both points are vertices of the same triangle. For example, even if C and D were near each other, CD wouldn't be a side because C belongs to triangle ABC and D belongs to triangle DEF.

How many sides does each triangle have?

Every triangle has exactly three sides. Triangle ABC has sides AB, BC, and AC. Triangle DEF has sides DE, EF, and DF. That's it - no more, no less!

Can I just look at the diagram to see the sides?

Yes! The sides are the line segments you can see drawn between vertices. But always double-check by naming - if you can see a line connecting two vertices of the same triangle, that's a side.

What if the triangles share a vertex?

Even if triangles share a vertex, their sides are still separate. Each triangle's sides only connect its own three vertices. Shared vertices don't create shared sides between different triangles.

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