To solve the question of counting the number of edges in each of the specified three-dimensional figures, we will analyze each shape step by step.
### Step 1: Tetrahedron
A tetrahedron is a polyhedron with four triangular faces. It has:
- **Vertices**: 4 (let's name them A, B, C, D)
- **Edges**: Each vertex connects to every other vertex.
To count the edges:
- From vertex A, we can draw edges to B, C, and D (3 edges).
- From vertex B, we can draw edges to C and D (2 edges, as AB is already counted).
- From vertex C, we can draw an edge to D (1 edge, as AC and BC are already counted).
Thus, the total number of edges is:
\[
3 + 2 + 1 = 6
\]
### Step 2: Rectangular Pyramid
A rectangular pyramid has a rectangular base and four triangular faces. It has:
- **Vertices**: 5 (let's name them A, B, C, D for the rectangle and E for the apex)
- **Edges**:
- The base rectangle has 4 edges: AB, BC, CD, DA.
- Each vertex of the rectangle connects to the apex E, adding 4 more edges: AE, BE, CE, DE.
Thus, the total number of edges is:
\[
4 + 4 = 8
\]
### Step 3: Cube
A cube is a three-dimensional shape with six square faces. It has:
- **Vertices**: 8 (let's name them A, B, C, D, E, F, G, H)
- **Edges**:
- Each face of the cube has 4 edges, and there are 6 faces. However, each edge is shared by 2 faces.
Thus, the total number of edges is:
\[
\frac{6 \times 4}{2} = 12
\]
### Step 4: Triangular Prism
A triangular prism has two triangular bases and three rectangular lateral faces. It has:
- **Vertices**: 6 (let's name them A, B, C for one triangle and D, E, F for the other triangle)
- **Edges**:
- Each triangular base has 3 edges: AB, BC, CA for the first triangle and DE, EF, FD for the second triangle.
- There are 3 edges connecting the corresponding vertices of the triangles: AD, BE, CF.
Thus, the total number of edges is:
\[
3 + 3 + 3 = 9
\]
### Final Summary of Edges
- **Tetrahedron**: 6 edges
- **Rectangular Pyramid**: 8 edges
- **Cube**: 12 edges
- **Triangular Prism**: 9 edges
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