Two-dimensional (2D) refers to shapes and figures that exist in two dimensions - length and width. These shapes are flat and have no depth. Some common 2D shapes include squares, rectangles, triangles, circles, and polygons.

Each 2D shape has its own unique properties, including:

**Number of Sides:**The number of sides or edges a shape has.**Angles:**The angles formed by the intersection of the shape's sides.**Area:**The amount of space inside the shape.**Perimeter:**The total length of the shape's boundary.

When studying two-dimensional geometry, it's important to understand the following concepts:

- Identifying and classifying 2D shapes based on their properties.
- Calculating the area and perimeter of different 2D shapes.
- Understanding the relationships between different 2D shapes, such as how they can be combined or split to form new shapes.
- Applying 2D geometry concepts to solve real-world problems, such as calculating the area of a room or the perimeter of a garden.

Practice drawing and visualizing 2D shapes, and work through plenty of example problems to reinforce your understanding of the concepts.

Remember to review the formulas for calculating the area and perimeter of common 2D shapes, and make sure to understand how to apply these formulas in different scenarios.

By mastering the properties and calculations related to 2D shapes, you'll be well-prepared to tackle more advanced geometry concepts in the future.

.Study GuideSimilarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer keyUsing Similar Polygons Worksheet/Answer keySimilar Polygons Worksheet/Answer keyUsing Similar Polygons Worksheet/Answer keySimilar Polygons

Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Understand and use ratios and proportions to represent quantitative relationships.

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.

Apply transformations and use symmetry to analyze mathematical situations.

Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling.

Measurement (NCTM)

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

Solve problems involving scale factors, using ratio and proportion.

Grade 8 Curriculum Focal Points (NCTM)

Geometry and Measurement: Analyzing two- and three-dimensional space and figures by using distance and angle

Students use fundamental facts about distance and angles to describe and analyze figures and situations in two- and three-dimensional space and to solve problems, including those with multiple steps. They prove that particular configurations of lines give rise to similar triangles because of the congruent angles created when a transversal cuts parallel lines. Students apply this reasoning about similar triangles to solve a variety of problems, including those that ask them to find heights and distances. They use facts about the angles that are created when a transversal cuts parallel lines to explain why the sum of the measures of the angles in a triangle is 180 degrees, and they apply this fact about triangles to find unknown measures of angles. Students explain why the Pythagorean Theorem is valid by using a variety of methods - for example, by decomposing a square in two different ways. They apply the Pythagorean Theorem to find distances between points in the Cartesian coordinate plane to measure lengths and analyze polygons and polyhedra.