In mathematics, a shape is a geometric figure that can be described by its outline, area, and other properties. Shapes can be two-dimensional (2D) or three-dimensional (3D).

**Triangle:**A polygon with three edges and three vertices.**Square:**A four-sided polygon with all sides of equal length and all angles of 90 degrees.**Rectangle:**A four-sided polygon with opposite sides of equal length and all angles of 90 degrees.**Circle:**A shape with all points the same distance from its center.**Pentagon:**A five-sided polygon.**Hexagon:**A six-sided polygon.

**Sphere:**A three-dimensional shape that is perfectly round, like a ball.**Cube:**A three-dimensional shape with six square faces, twelve straight edges, and eight vertices.**Cylinder:**A three-dimensional shape with two parallel circular bases connected by a curved surface.**Cone:**A three-dimensional shape with a circular base that tapers to a point at the top.**Rectangular Prism:**A three-dimensional shape with six faces, each of which is a rectangle.

Shapes have various properties, including perimeter, area, volume, and angles. Understanding these properties is important for solving problems involving shapes.

- Memorize the names and properties of common 2D and 3D shapes.
- Practice calculating the perimeter and area of different shapes.
- Understand the formulas for calculating the volume of 3D shapes.
- Use visual aids, such as diagrams and models, to understand the characteristics of different shapes.
- Practice solving problems involving shapes to strengthen your understanding of the concepts.

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.