Interactive worksheet for learning the properties of 3D shapes.

It looks like you've uploaded a worksheet titled "Properties of 3D Shapes" that asks students to identify the number of edges, vertices, and faces for various 3D shapes. Below is a completed version of the worksheet with explanations.

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🔷 Worksheet: Properties of 3D Shapes

We’ll go through each shape one by one, fill in the blanks, and explain how we get the values.

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#### 1. Yellow Pyramid (Square-Based Pyramid)
- Name: Square-Based Pyramid
- Edges: 8
- 4 edges on the base (square), and 4 edges from the base corners to the apex.
- Vertices: 5
- 4 vertices on the square base + 1 apex.
- Faces: 5
- 1 square base + 4 triangular faces.

✔ Answer: Edges = 8, Vertices = 5, Faces = 5

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#### 2. Red Sphere
- Name: Sphere
- Edges: 0
- A sphere has no straight edges.
- Vertices: 0
- No corners or points.
- Faces: 0
- A sphere is a smooth curved surface; not made of flat faces.

✔ Answer: Edges = 0, Vertices = 0, Faces = 0

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#### 3. Blue Shape (Triangular Prism)
- Name: Triangular Prism
- Edges: 9
- 3 edges on the top triangle, 3 on the bottom triangle, and 3 connecting the corresponding vertices.
- Vertices: 6
- 3 on top, 3 on bottom.
- Faces: 5
- 2 triangular bases + 3 rectangular lateral faces.

✔ Answer: Edges = 9, Vertices = 6, Faces = 5

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#### 4. Pink Shape (Cube)
- Name: Cube
- Edges: 12
- Each face has 4 edges, but shared → 6 faces × 4 edges / 2 = 12.
- Vertices: 8
- Corners of the cube.
- Faces: 6
- 6 square faces.

✔ Answer: Edges = 12, Vertices = 8, Faces = 6

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#### 5. Cyan Cone
- Name: Cone
- Edges: 1 (if considering the circular edge)
- Technically, a cone has 1 curved edge at the base (but sometimes considered 0 in elementary contexts).
- However, in standard elementary math, cones are often said to have 0 edges because they don’t have straight edges.
- Vertices: 1
- The tip (apex) is a vertex.
- Faces: 2
- 1 curved surface + 1 circular base.

⚠️ Note: There's some ambiguity here due to definitions:
- In basic geometry:
- Edges: 0 (no straight lines)
- Vertices: 1
- Faces: 2 (base + curved surface)

✔ Answer: Edges = 0, Vertices = 1, Faces = 2

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#### 6. Green Shape (Triangular Pyramid / Tetrahedron)
- Name: Triangular Pyramid (Tetrahedron)
- Edges: 6
- Each of the 4 triangular faces shares edges → 4×3 / 2 = 6 edges.
- Vertices: 4
- One at each corner.
- Faces: 4
- All triangular.

✔ Answer: Edges = 6, Vertices = 4, Faces = 4

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#### 7. Cylinder (Green)
- Name: Cylinder
- Edges: 0 (or 2 if counting circular edges)
- In basic terms, cylinders have 0 edges (no straight lines).
- But some curricula count the top and bottom circles as edges → 2.
- We'll use 0 for simplicity in this context.
- Vertices: 0
- No corners.
- Faces: 3
- 1 curved surface + 2 circular bases.

✔ Answer: Edges = 0, Vertices = 0, Faces = 3

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#### 8. Yellow Cube (Same as earlier)
- Name: Cube
- Already covered above:
- Edges = 12
- Vertices = 8
- Faces = 6

✔ Same as #4.

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✔ Final Completed Table:

| Shape | Edges | Vertices | Faces |
|------------------------|-------|----------|-------|
| Square-Based Pyramid | 8 | 5 | 5 |
| Sphere | 0 | 0 | 0 |
| Triangular Prism | 9 | 6 | 5 |
| Cube | 12 | 8 | 6 |
| Cone | 0 | 1 | 2 |
| Triangular Pyramid | 6 | 4 | 4 |
| Cylinder | 0 | 0 | 3 |
| Cube (again) | 12 | 8 | 6 |

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🔍 Summary of Key Concepts:

- Face: A flat surface of a 3D shape.
- Edge: A line segment where two faces meet.
- Vertex (plural: vertices): A corner where edges meet.

> 🧠 Tip: Use Euler’s Formula for polyhedra:
> V – E + F = 2
> (Works for most 3D shapes without holes, like cubes, pyramids, prisms).
> Example: Cube → 8 – 12 + 6 = 2 ✔

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