Diagonals are line segments that connect non-adjacent vertices of a polygon. They are important in geometry and can help us to understand the properties of various shapes.

The types of diagonals depend on the shape of the polygon:

**Rectangle:**A rectangle has two diagonals of equal length, and each diagonal bisects the other. The length of the diagonal can be calculated using the Pythagorean theorem.**Square:**A square is a special type of rectangle, so it also has two equal diagonals that bisect each other.**Parallelogram:**A parallelogram has two diagonals that bisect each other. The diagonals are not necessarily equal in length.**Rhombus:**A rhombus is a special type of parallelogram, so it has two diagonals that bisect each other and are of equal length.**Trapezoid:**A trapezoid has one diagonal, which is the line segment connecting the non-parallel sides.**Pentagon, Hexagon, etc.:**The number of diagonals in polygons with more than four sides can be calculated using the formula:*n(n-3)/2*, where*n*is the number of sides.

Diagonals have several properties that are useful in geometry:

- They divide the polygon into triangles, which can help in calculating the area of the polygon.
- In a rectangle or square, the diagonals are equal in length and bisect each other, forming four right angles at their point of intersection.
- In a parallelogram or rhombus, the diagonals bisect each other but are not necessarily equal in length.
- The length of a diagonal in a rectangle or square can be calculated using the Pythagorean theorem:
*d = √(l^2 + w^2)*, where*d*is the length of the diagonal,*l*is the length, and*w*is the width of the rectangle.

When studying diagonals in geometry, it's important to remember the specific properties of diagonals in different types of polygons. Practice calculating the length of diagonals in rectangles and squares using the Pythagorean theorem. Understand how diagonals divide polygons into triangles and how they can help in finding the area of the polygon. Also, practice using the formula to calculate the number of diagonals in polygons with more than four sides.

It's helpful to work through example problems and exercises to reinforce your understanding of diagonals and their properties in geometry.

.Study GuideMeasurement, Perimeter, and Circumference Worksheet/Answer key

Measurement, Perimeter, and Circumference Worksheet/Answer key

Measurement, Perimeter, and Circumference Worksheet/Answer key

Measurement, Perimeter, and Circumference

Geometry (NCTM)

Use visualization, spatial reasoning, and geometric modeling to solve problems.

Use geometric models to represent and explain numerical and algebraic relationships.

Measurement (NCTM)

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

Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision.

Develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles and develop strategies to find the area of more-complex shapes.

Connections to the Grade 7 Focal Points (NCTM)

Measurement and Geometry: Students connect their work on proportionality with their work on area and volume by investigating similar objects. They understand that if a scale factor describes how corresponding lengths in two similar objects are related, then the square of the scale factor describes how corresponding areas are related, and the cube of the scale factor describes how corresponding volumes are related. Students apply their work on proportionality to measurement in different contexts, including converting among different units of measurement to solve problems involving rates such as motion at a constant speed. They also apply proportionality when they work with the circumference, radius, and diameter of a circle; when they find the area of a sector of a circle; and when they make scale drawings.