Edges are the lines or line segments where the faces of a 3-dimensional shape meet. They are the intersection of two faces on a solid figure. Understanding edges is important in geometry as it helps in identifying and classifying different 3D shapes.

There are two types of edges:

**Visible Edges:**These are the edges that are visible from a particular viewpoint. They are the outlines of the solid figure that we can see.**Hidden Edges:**These are the edges that are not visible from a particular viewpoint. They are hidden behind other faces of the solid figure.

Let's look at some common 3D shapes and their edges:

**Cube:**A cube has 12 edges, where each edge is a line segment where two faces meet.**Cylinder:**A cylinder has 2 edges - one around the circular base and one along the height of the cylinder.**Sphere:**A sphere has no edges, as it is a curved surface with no flat faces.**Cuboid:**A cuboid has 12 edges, similar to a cube, but its faces are rectangular instead of square.

When studying edges in geometry, it's important to:

- Understand the definition of an edge and how it relates to solid figures.
- Be able to identify and count the number of edges in common 3D shapes.
- Practice visualizing and drawing the visible and hidden edges of different solid figures.
- Apply the concept of edges to solve problems involving surface area, volume, and spatial reasoning.

Remember, edges are an essential part of understanding the properties and characteristics of 3D shapes in geometry.

.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.