Triangle Side AB: Identifying Line Segments Between Two Similar Triangles

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

Look at the triangle outlines in the diagram. Points A, B, and C form the left triangle, while points D, E, and F form the right triangle. Each triangle has exactly three vertices.

Q: Can two points from different triangles form a side?

No! A triangle side can only connect two vertices that belong to the same triangle. For example, A and E cannot form a triangle side because they're in different triangles.

Q: What if I can't see the line connecting two points clearly?

Focus on the triangle structure rather than individual lines. If two points are vertices of the same triangle, there must be a side connecting them, even if it's hard to see in the diagram.

Q: Are there any other sides in the left triangle besides AB?

Yes! The left triangle has three sides: $ AB $, $ BC $, and $ AC $. Each side connects two of the three vertices A, B, and C.

Q: How can I remember which letters go with which triangle?

Use the alphabetical pattern: The left triangle uses the first three letters (A, B, C), and the right triangle uses the next three letters (D, E, F). This makes it easier to keep track!

Triangle Side Identification with Multiple Vertices

Look at the two triangles below.

Is AB 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 AB a side of one of the triangles?

Step-by-step solution

To solve this problem, we will inspect the two triangles in the diagram to determine if $AB$ can be identified as one of their sides.

1. We begin by examining the triangle on the left side, which is formed by points $A$ , $B$ , and $C$ .
- Point $A$ is located at the top of the triangle, while point $B$ is at the bottom left.
- The diagram clearly shows a direct line connecting point $A$ to point $B$ , therefore forming a side of this triangle.

2. There is another triangle on the right side of the diagram formed by points $D$ , $E$ , and $F$ . However, since points $A$ and $B$ are not involved in this triangle, they cannot form a side of it.

Hence, it is evident that $AB$ is indeed a side of the left triangle, comprising points $A$ , $B$ , and $C$ .

Therefore, the answer to the problem is Yes.

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic

Definition: A triangle side connects two vertices of that triangle
Method: Check if both points A and B belong to same triangle
Verification: Trace the line from A to B on the diagram ✓

Common Mistakes

Avoid these frequent errors

Assuming any two labeled points form a triangle side
Don't connect any two points just because they have letters = wrong triangle identification! Points must belong to the same triangle to form its side. Always check which triangle contains both vertices before identifying 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 points belong to which triangle?

Look at the triangle outlines in the diagram. Points A, B, and C form the left triangle, while points D, E, and F form the right triangle. Each triangle has exactly three vertices.

Can two points from different triangles form a side?

No! A triangle side can only connect two vertices that belong to the same triangle. For example, A and E cannot form a triangle side because they're in different triangles.

What if I can't see the line connecting two points clearly?

Focus on the triangle structure rather than individual lines. If two points are vertices of the same triangle, there must be a side connecting them, even if it's hard to see in the diagram.

Are there any other sides in the left triangle besides AB?

Yes! The left triangle has three sides: $AB$ , $BC$ , and $AC$ . Each side connects two of the three vertices A, B, and C.

How can I remember which letters go with which triangle?

Use the alphabetical pattern: The left triangle uses the first three letters (A, B, C), and the right triangle uses the next three letters (D, E, F). This makes it easier to keep track!

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