A square is a four-sided polygon (quadrilateral) with four right angles and four equal sides. In a square, opposite sides are parallel and equal in length, and all interior angles measure 90 degrees.

**Equal sides:**All four sides of a square are of equal length.**Right angles:**All four angles in a square are right angles (90 degrees).**Diagonals:**The diagonals of a square are equal in length and bisect each other at right angles.**Area:**The area of a square is calculated using the formula:*Area = side x side*or*Area = side*.^{2}**Perimeter:**The perimeter of a square is calculated by adding the lengths of all four sides:*Perimeter = 4 x side*.

1. Find the area and perimeter of a square with side length 5 units.

2. If the area of a square is 49 square meters, find the length of each side.

3. A square has a perimeter of 24 cm. Find the length of each side and the area of the square.

- Memorize the formulas for finding the area and perimeter of a square.

- Practice drawing and identifying squares based on their properties.

- Work through example problems to understand how to apply the formulas in various situations.

- Understand the relationship between the side length, area, and perimeter of a square.

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.