In geometry, a diagonal is a line segment that connects two non-adjacent vertices of a polygon. The most common polygons that have diagonals are quadrilaterals, such as squares, rectangles, parallelograms, and rhombuses. Diagonals can also be found in other polygons, such as pentagons, hexagons, and so on.

**Square:**A square has two diagonals that are congruent, perpendicular, and bisect each other.**Rectangle:**A rectangle has two diagonals that are congruent.**Parallelogram:**A parallelogram has two diagonals that bisect each other.**Rhombus:**A rhombus has diagonals that are perpendicular and bisect each other at right angles.

The length of a diagonal can be found using the Pythagorean theorem. For example, in a rectangle, if the length and width are given, the length of the diagonal can be calculated using the formula:

Diagonal length = √(length^{2} + width^{2})

To study diagonals in polygons, follow these steps:

- Understand the definition of a diagonal and its properties in different types of polygons.
- Practice using the Pythagorean theorem to find the length of a diagonal in rectangles and other right-angled polygons.
- Solve problems involving diagonals in various types of quadrilaterals to reinforce your understanding of their properties.
- Explore diagonals in other polygons, such as pentagons and hexagons, to see how the concept extends beyond quadrilaterals.

Remember, understanding the concept of diagonals in polygons is important for geometry and can be applied to various real-world situations involving shapes and structures.

.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.