Triangle Side Verification: Is BD a Side of Triangle BCD?

Question

True or false:

BD is a side of triangle BCD.

Video Solution

Solution Steps

00:00 Determine whether BD is a side in the given triangle BCD
00:03 Identify the sides of the triangle BCD
00:06 Each combination of two letters represents a side in the triangle
00:10 Proceed to examine all of the potential combinations in order to identify all of the sides (There are a total of 3 sides)
00:16 Therefore, we can observe that BD is part of triangle BCD
00:20 This is the solution

Step-by-Step Solution

To ascertain whether BD is a side of triangle BCD, observe the basic geometric principles associated with triangles.

In Euclidean geometry, a triangle is named based on its vertices. For triangle BCD, it consists of three vertices: B, C, and D.

The sides of the triangle are the line segments directly joining these vertices. Thus, the sides of triangle BCD are:

  • Line segment BC, connecting vertices B and C.
  • Line segment CD, connecting vertices C and D.
  • Line segment BD, connecting vertices B and D.

Line segments such as BD connect two vertices within the triangle and thus qualify as one of its sides. This aligns with the standard definition of a triangle in Euclidean geometry, where any side is formed by connecting two of its vertices.

Therefore, indeed, BD is a side of triangle BCD.

The correct conclusion is true: BD is a side of triangle BCD.

Answer

True

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