Perpendicular lines are two lines that intersect at a 90-degree angle. This means that if you were to measure the angles formed by the intersection of the lines, you would find that they are each 90 degrees.

- Perpendicular lines have slopes that are negative reciprocals of each other. If the slope of one line is m, then the slope of a line perpendicular to it is -1/m.
- When graphed on the coordinate plane, perpendicular lines form a "L" shape where they intersect.
- Perpendicular lines are commonly denoted by the symbol ⊥, which is placed between the lines to show that they are perpendicular.

Consider two lines with slopes m1 = 2 and m2 = -1/2. These slopes are negative reciprocals of each other, so the lines are perpendicular.

In order to understand perpendicular lines, it's important to grasp the concept of slope and how it relates to the angle of intersection between two lines. Practice finding the slope of various lines and identifying when lines are perpendicular based on their slopes. Additionally, work on graphing perpendicular lines on the coordinate plane and identifying the 90-degree angle formed by their intersection.

Remember to also study the properties of perpendicular lines and how they relate to geometric shapes and angles. This will help reinforce your understanding of the concept.

.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.