An equation is a mathematical statement that shows the equality of two expressions. It consists of two sides separated by an equals sign (=).

There are different types of equations, including:

**Linear Equations:**Equations of the form ax + b = c, where a, b, and c are constants and x is the variable.**Quadratic Equations:**Equations of the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable.**Exponential Equations:**Equations involving exponential functions, such as 2^x = 16.**Trigonometric Equations:**Equations involving trigonometric functions, such as sin(x) = 0.5.

To solve an equation, you aim to find the value of the variable that makes the equation true. This involves performing operations to isolate the variable on one side of the equation.

**Combine Like Terms:**Combine similar terms on each side of the equation.**Isolate the Variable:**Use inverse operations (addition, subtraction, multiplication, division) to isolate the variable on one side of the equation.**Check Your Solution:**Substitute the value found for the variable back into the original equation to ensure it satisfies the equality.

Some important properties of equations include:

**Reflexive Property:**For any real number a, a = a.**Symmetric Property:**If a = b, then b = a.**Transitive Property:**If a = b and b = c, then a = c.

Equations are used in various real-life scenarios, such as calculating distances, solving for unknown quantities in science and engineering, and modeling physical phenomena.

.Study GuideSimilarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

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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.