A polygon is a closed shape with straight sides. The sides of a polygon are line segments, and the place where two sides meet is called a vertex. Polygons are named by the number of sides they have. For example, a polygon with three sides is called a triangle, a polygon with four sides is called a quadrilateral, and so on.

There are several types of polygons based on the number of sides they have:

**Triangle:**A polygon with three sides.**Quadrilateral:**A polygon with four sides.**Pentagon:**A polygon with five sides.**Hexagon:**A polygon with six sides.**Heptagon (or Septagon):**A polygon with seven sides.**Octagon:**A polygon with eight sides.**Nonagon (or Enneagon):**A polygon with nine sides.**Decagon:**A polygon with ten sides.

Here are some important properties of polygons:

**Interior Angles:**The sum of the interior angles of a polygon with*n*sides is given by the formula:*(n - 2) * 180 degrees*.**Exterior Angles:**The sum of the exterior angles of any polygon is always 360 degrees.**Diagonals:**A diagonal is a line segment that connects two non-adjacent vertices of a polygon. The number of diagonals in a polygon can be calculated using the formula:*n(n-3)/2*, where*n*is the number of sides.

When studying polygons, it's important to:

- Memorize the names and properties of common polygons, including triangles, quadrilaterals, pentagons, hexagons, and octagons.
- Understand the formulas for calculating interior and exterior angles, as well as the number of diagonals in a polygon.
- Practice identifying and drawing different types of polygons.
- Solve problems involving the properties of polygons, such as finding missing angles or sides.

Understanding polygons is essential in geometry and lays the foundation for more advanced concepts in mathematics.

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.