In mathematics, three-dimensional (3D) shapes are objects that have three dimensions - length, width, and height. These shapes are also called solids because they have a solid shape or form, as opposed to two-dimensional shapes which are flat. Understanding three-dimensional shapes is important in geometry and can help us understand the world around us in a more detailed way.

**Faces:**The flat surfaces of a 3D shape. A cube, for example, has 6 faces.**Edges:**The lines where two faces of a 3D shape meet. A cube has 12 edges.**Vertices:**The points where three or more edges of a 3D shape meet. A cube has 8 vertices.

There are many three-dimensional shapes, but some common ones include:

**Cube:**A six-sided shape where each side is a square.**Cuboid:**Similar to a cube, but with rectangular faces instead of square faces.**Sphere:**A perfectly round shape, like a ball.**Cylinder:**A shape with two circular faces and a curved surface.**Cone:**A shape with a circular base and a single curved surface.**Pyramid:**A polyhedron with a polygon base and triangular faces that meet at a single vertex.

To better understand three-dimensional shapes, it's important to practice identifying and visualizing them. Here are some steps you can take to study this topic:

- Memorize the names, faces, edges, and vertices of common 3D shapes.
- Practice drawing and sketching different 3D shapes from different angles to improve your visualization skills.
- Explore real-world objects that resemble 3D shapes and identify their characteristics.
- Solve problems and exercises related to calculating the surface area and volume of 3D shapes to deepen your understanding.
- Use interactive online tools and resources to manipulate and explore 3D shapes in a virtual environment.

By mastering the concepts and properties of three-dimensional shapes, you will develop a strong foundation in geometry and be able to apply this knowledge in various real-world scenarios.

.Study GuideGeometric Proportions Worksheet/Answer key

Geometric Proportions Worksheet/Answer key

Geometric Proportions Worksheet/Answer key

Geometric Proportions Worksheet/Answer key Numerical & Geometric Proportions

Number and Operations (NCTM)

Compute fluently and make reasonable estimates.

Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

Geometry (NCTM)

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects.

Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.

Measurement (NCTM)

Apply appropriate techniques, tools, and formulas to determine measurements.

Solve problems involving scale factors, using ratio and proportion.

Connections to the Grade 7 Focal Points (NCTM)

Measurement and Geometry: Students connect their work on proportionality with their work on area and volume by investigating similar objects. They understand that if a scale factor describes how corresponding lengths in two similar objects are related, then the square of the scale factor describes how corresponding areas are related, and the cube of the scale factor describes how corresponding volumes are related. Students apply their work on proportionality to measurement in different contexts, including converting among different units of measurement to solve problems involving rates such as motion at a constant speed. They also apply proportionality when they work with the circumference, radius, and diameter of a circle; when they find the area of a sector of a circle; and when they make scale drawings.