Parts of a Triangle: Identifying sides in a triangle

To solve this problem, let's clarify the role of AB in the context of triangle ABC by analyzing its diagram:

• Step 1: Identify the vertices of the triangle. According to the diagram, the vertices of the triangle are points labeled A, B, and C.
• Step 2: Determine the sides of the triangle. In any triangle, the sides are the segments connecting pairs of distinct vertices.
• Step 3: Identify AB as a line segment connecting vertex A and vertex B, labeled directly in the diagram.

Considering these steps, line segment AB connects vertex A with vertex B, and hence, forms one of the sides of the triangle ABC. Therefore, AB is indeed a side of triangle ABC as shown in the diagram.

The conclusion here is solidly supported by our observation of the given triangle. Thus, the statement that AB is a side of the triangle ABC is True.

To determine if line segment AD is a side of triangle ABC, we need to agree on the definition of a triangle's side. A triangle consists of three sides, each connecting pairs of its vertices. In triangle ABC, these sides are AB, BC, and CA. Each side is composed of a direct line segment connecting the listed vertices.

In the diagram provided, there is no indication of a point D connected to point A or any other vertex of triangle ABC. To claim AD as a side, D would need to be one of the vertices B or C, or a commonly recognized point forming part of the triangle’s defined structure. The provided figure and description do not support that AD exists within the given triangle framework, as no point D is defined within or connecting any existing vertices.

Therefore, according to the problem's context and based on the definition of the sides of a triangle, AD cannot be considered a side of triangle ABC. It follows that the statement "AD is a side of triangle ABC" should be deemed not true.

To solve this problem, we must determine whether BC is indeed a side of triangle ABC. A triangle consists of three vertices connected by three line segments that form its sides.

Firstly, observe the triangle labeled in the diagram with vertices A, B, and C. For triangle ABC, the sides are composed of the segments that connect these points.

• The three line segments connecting the vertices are:
  • $AB$, connecting points A and B;
  • $BC$, connecting points B and C; and
  • $CA$, connecting points C and A.

Among these, BC is clearly listed as one of the segments connecting two vertices of the triangle. Therefore, BC is indeed a side of triangle ABC.

Hence, the statement is True.

To solve this problem, consider the following:

• The figure provided illustrates a triangle labeled ABD. In a triangle, the sides are defined as the line segments connecting its vertices.
• In triangle ABD, the vertices are points A, B, and D.
• The sides of this triangle are the segments AB, AD, and BD.
• Since AB is a direct connection between vertices A and B, it is indeed one of the sides of triangle ABD.

After analyzing the figure and definition of a triangle's sides, we can conclude that the answer is correct.

Therefore, the correct answer is True.

The problem asks if line segment DC is a side of triangle ABD.

In triangle geometry, the sides of a triangle are the segments connecting its vertices. Here, the triangle ABD is formed by vertices A, B, and D.

Upon observing the diagram:

• The vertices of triangle ABD are A, B, and D.
• The sides of triangle ABD are AB, BD, and AD.
• The segment DC connects points D and C, which are not both vertices of triangle ABD.

Therefore, line segment DC is not a side of triangle ABD.

The statement "DC is a side of triangle ABD" is False.

Let's determine if DC is a side of triangle BDC:

First, we need to identify the triangle BDC:

• Vertices of triangle BDC are: $B, D,$ and $C$.
• Sides of triangle BDC are the line segments that connect these points. Namely, these sides are $BD, DC,$ and $BC$.

Since $DC$ is one of the line segments connecting the vertices of triangle BDC, it indeed constitutes one of its sides.

Therefore, we conclude that the statement is true: DC is a side of the triangle BDC.

To determine whether AC is a side of triangle BDC, let us take the following steps:

• Identify the vertices of triangle BDC, which are points B, D, and C.
• Consider the sides of triangle BDC which are BD, DC, and BC, as each side is formed by connecting two vertices of the triangle.

Analysis:

Triangle BDC has exactly three sides, formed by the segments connecting vertices B, D, and C, which are:

• BD (connecting vertices B and D)
• DC (connecting vertices D and C)
• BC (connecting vertices B and C)

Since segment AC does not connect any two vertices of triangle BDC, it cannot be a side of this triangle.

Thus, the statement "AC is a side of triangle BDC" is False.

Therefore, the solution to the problem is False.

To solve this problem, we begin by recalling that a triangle is defined by three vertices, and the sides of the triangle are the line segments connecting these vertices. In $\triangle ABD$, the vertices are $A$, $B$, and $D$. The sides of the triangle are therefore the segments that connect these points in pairs.

Let us now consider each segment that forms the sides of $\triangle ABD$:

• AB connects vertices $A$ and $B$.
• BD connects vertices $B$ and $D$.
• AD connects vertices $A$ and $D$.

Since line segment $BD$ connects two of the vertices of the triangle ($B$ and $D$), it is one of the sides of $\triangle ABD$ by definition.

Therefore, the statement "BD is a side of the triangle ABD" is True.

To solve this problem, we start by examining the notation typically associated with a triangle and its sides. In standard geometric practice, the sides of a triangle are denoted by referring to the two vertices that form the endpoints of each side. For triangle ABC, the sides could normally be expressed as AB, BC, or CA.

The question proposes that "DC" is a side of triangle ABC. To analyze this, we consider the vertices of triangle ABC: A, B, and C. For "DC" to be considered a side, D must be an additional point that is explicitly mentioned or defined in the context of triangle ABC. However, the problem simply provides triangle "ABC" with no indication of point D being relevant in the triangle's primary structure of three vertices and three sides.

Given the lack of provision or clarification on point D's involvement in triangle ABC, side "DC" cannot logically be deduced as one of its sides because the naming convention explicitly bounds the potential sides to those vertices within the triangle, namely A, B, and C.

Therefore, based on our analysis and understanding of geometric conventions, the statement “DC is the side of triangle ABC” is not true.

Therefore, the correct answer to the problem is Not true.

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.