Triangle Side Identification: Locating Line Segment DF in Given Triangles

Triangle Side Recognition with Multiple Vertices

Look at the two triangles below.

Is DF a side in one of the triangles?

AAABBBCCCDDDEEEFFF

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Look at the two triangles below.

Is DF a side in one of the triangles?

AAABBBCCCDDDEEEFFF

2

Step-by-step solution

To determine if DF is a side in one of the triangles, we need to look at the vertices that define each triangle:

  • Triangle 1: Vertices A, B, C
  • Triangle 2: Vertices D, E, F

By identifying these vertices, we can list the triangle sides:

  • For Triangle 1, the sides are: AB, BC, and CA.
  • For Triangle 2, the sides are: DE, EF, and FD.

In Triangle 2, the segment DF is the same as FD, which confirms it is indeed a side of this triangle.

Therefore, the solution to the problem is yes, DF is a side of one of the triangles.

3

Final Answer

Yes.

Key Points to Remember

Essential concepts to master this topic
  • Triangle Definition: A triangle has exactly three sides connecting three vertices
  • Side Identification: List all vertices like Triangle DEF has sides DE, EF, and FD
  • Verification: Check both triangles systematically for the target segment DF or FD ✓

Common Mistakes

Avoid these frequent errors
  • Not checking both possible vertex orders
    Don't look only for DF in exact order = missing the answer! Side DF is the same as side FD, just written with vertices in different sequence. Always check both vertex arrangements when identifying triangle sides.

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 vertices belong to each triangle?

+

Look carefully at the diagram and identify which points are connected by lines. Triangle ABC has vertices A, B, and C all connected to each other, while Triangle DEF has vertices D, E, and F connected.

Is DF the same as FD?

+

Yes, absolutely! A line segment connecting two points is the same regardless of which vertex you name first. DF and FD represent the exact same side of the triangle.

How many sides does each triangle have?

+

Every triangle has exactly three sides. Triangle ABC has sides AB, BC, and CA. Triangle DEF has sides DE, EF, and FD (which is the same as DF).

What if I can't see the triangles clearly in the diagram?

+

Focus on the labeled vertices (the letters). Group them by which ones are connected: A-B-C forms one triangle, and D-E-F forms another triangle. The lines show these connections.

Do I need to worry about triangle size or shape?

+

No! Whether triangles are big, small, or different shapes, they still have the same three sides each. Just focus on identifying which vertices are connected to form each triangle.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Triangle questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations