Identify Line Segment AD: Triangle Vertex Connection Analysis

Q: How do I know which points belong to the same triangle?

Look at the diagram carefully! Triangle vertices are connected by lines forming the triangle's edges. Points A, B, C form one triangle, while D, E, F form another separate triangle.

Q: What's the difference between a line segment and a triangle side?

A triangle side is a specific line segment that connects two adjacent vertices of the same triangle. Not every line segment between two points is a triangle side - it must be part of the triangle's boundary.

Q: Can I connect any two points in the diagram?

You can draw a line segment between any two points, but that doesn't make it a triangle side. Only segments that form the actual edges of a triangle count as its sides.

Q: How do I list all sides of a triangle systematically?

For triangle ABC, go around the triangle: AB, BC, CA. For triangle DEF: DE, EF, FD. This ensures you don't miss any sides or count extras.

Q: What if the triangles share a vertex?

Even if triangles share a vertex, they're still separate triangles with their own distinct sides. A line segment connecting vertices from different triangles is not a side of either triangle.

Triangle Analysis with Line Segment Classification

Look at the two triangles below.

Is AD 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 AD a side of one of the triangles?

Step-by-step solution

The task is to determine if the segment $AD$ is a side of any of the given triangles. Based on the diagram, we have two distinct triangles:

$\triangle ABC$ : Formed by the points $A, B, C$ .
$\triangle DEF$ : Formed by the points $D, E, F$ .

For $\triangle ABC$ , the sides are $AB, BC,$ and $CA$ .

For $\triangle DEF$ , the sides are $DE, EF,$ and $FD$ .

In analyzing both triangles, we observe that:

The side $AD$ is not listed as one of the sides of either triangle.

Thus, the conclusion is clear: AD is not a side of either triangle.

Therefore, the answer is No.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Triangle Sides: Each triangle has exactly three sides connecting its vertices
Identification: List all sides systematically: Triangle ABC has AB, BC, CA
Verification: Check if segment connects vertices from same triangle ✓

Common Mistakes

Avoid these frequent errors

Assuming any two points form a triangle side
Don't connect any two labeled points and call it a triangle side = wrong classification! Points from different triangles don't form sides of either triangle. Always identify which vertices belong to the same triangle first.

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 belong to the same triangle?

Look at the diagram carefully! Triangle vertices are connected by lines forming the triangle's edges. Points A, B, C form one triangle, while D, E, F form another separate triangle.

What's the difference between a line segment and a triangle side?

A triangle side is a specific line segment that connects two adjacent vertices of the same triangle. Not every line segment between two points is a triangle side - it must be part of the triangle's boundary.

Can I connect any two points in the diagram?

You can draw a line segment between any two points, but that doesn't make it a triangle side. Only segments that form the actual edges of a triangle count as its sides.

How do I list all sides of a triangle systematically?

For triangle ABC, go around the triangle: AB, BC, CA. For triangle DEF: DE, EF, FD. This ensures you don't miss any sides or count extras.

What if the triangles share a vertex?

Even if triangles share a vertex, they're still separate triangles with their own distinct sides. A line segment connecting vertices from different triangles is not a side of either triangle.

Is AD ever a side of these triangles?

No - A belongs to triangle ABC and D belongs to triangle DEF. Since they're from different triangles, AD cannot be a side of either triangle.

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