Triangle BDC Analysis: Is DE a Valid Side Segment?

Q: What makes a line segment a side of a triangle?

A triangle side must connect two adjacent vertices and form part of the triangle's perimeter. In triangle BDC, only segments BD, DC, and CB qualify as sides.

Q: Why isn't DE considered a side of triangle BDC?

DE connects points D and E, but E is not a vertex of triangle BDC. Triangle BDC only has vertices B, D, and C, so DE cannot be one of its sides.

Q: How do I identify all sides of any triangle?

List the three vertices in order, then identify the three connecting segments. For triangle XYZ, the sides are XY, YZ, and ZX - always connecting consecutive vertices.

Q: Can a triangle have more than three sides?

No! By definition, a triangle always has exactly three sides connecting its three vertices. Additional line segments in the diagram are not part of the triangle itself.

Q: What if there are extra points inside the triangle?

Extra points like E create additional segments but don't change the triangle's sides. Focus only on the segments connecting the triangle's three named vertices.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine whether DE is a side in the triangle BDC

00:04 Examine the letters of the triangle

00:15 Highlight all the sides of the triangle letter by letter

00:25 We can observe that DE is not part of our triangle

00:32 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Is DE a side in the triangle BDC?

2

Step-by-step solution

To solve this problem, we must analyze the provided geometric diagram carefully. The goal is to determine if line segment DE is a side of triangle BDC.

Let's examine the elements in the diagram:

Triangle BDC is outlined with vertices B, D, and C.
There is a line connecting points D and E, which does not coincide with the triangle's perimeter as sides are supposed to.
A clear check shows us that sides BDC are formed by line segments BD, DC, and CB in the triangle.
The line DE appears as an extension inside or outside of the triangle, making a clear indication that it is not part of the triangle itself.

Given the definition of a triangle's sides enclosed by its three vertices and the connectivity presented, it is apparent that DE is not recognized as one of the edges or sides that enclose triangle BDC.

Hence, the conclusion is: The statement "DE is a side in the triangle BDC" is Not true.

3

Final Answer

Not true

Key Points to Remember

Essential concepts to master this topic

Definition: Triangle sides connect adjacent vertices forming the perimeter boundary
Identification: Triangle BDC has sides BD, DC, and CB only
Verification: Check if segment connects two consecutive triangle vertices ✓

Common Mistakes

Avoid these frequent errors

Confusing internal segments with triangle sides
Don't assume any line segment inside or near a triangle is automatically a side = wrong identification! Internal segments like DE may connect points but don't form the triangle's boundary. Always check if the segment connects two consecutive vertices of the specific 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

What makes a line segment a side of a triangle?

+

A triangle side must connect two adjacent vertices and form part of the triangle's perimeter. In triangle BDC, only segments BD, DC, and CB qualify as sides.

Why isn't DE considered a side of triangle BDC?

+

DE connects points D and E, but E is not a vertex of triangle BDC. Triangle BDC only has vertices B, D, and C, so DE cannot be one of its sides.

How do I identify all sides of any triangle?

+

List the three vertices in order, then identify the three connecting segments. For triangle XYZ, the sides are XY, YZ, and ZX - always connecting consecutive vertices.

Can a triangle have more than three sides?

+

No! By definition, a triangle always has exactly three sides connecting its three vertices. Additional line segments in the diagram are not part of the triangle itself.

What if there are extra points inside the triangle?

+

Extra points like E create additional segments but don't change the triangle's sides. Focus only on the segments connecting the triangle's three named vertices.

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Triangle BDC Analysis: Is DE a Valid Side Segment?

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