What are Parallel Lines?
Parallel lines are two or more lines that are always the same distance apart and never meet. When graphed on a coordinate plane, parallel lines have the same slope but different y-intercepts.
Properties of Parallel Lines
- Equal Angles: When a transversal (a line that crosses two or more other lines) intersects parallel lines, corresponding angles, alternate interior angles, and alternate exterior angles are all congruent.
- Never Intersect: Parallel lines do not intersect, no matter how far they are extended.
- Equal Slopes: The slopes of parallel lines are always equal.
How to Identify Parallel Lines
To identify parallel lines, you can use the slope-intercept form of a line (y = mx + b), where 'm' represents the slope. If two lines have the same slope but different y-intercepts, they are parallel.
Study Guide
Here are some key points to remember when studying parallel lines:
- Understand the definition of parallel lines and how they behave when intersected by a transversal.
- Practice identifying parallel lines by comparing their slopes and y-intercepts.
- Memorize the properties of angles formed by parallel lines and a transversal.
- Work on exercises that involve identifying and working with parallel lines on coordinate planes.
◂Math Worksheets and Study Guides Sixth Grade. Volume
The resources above cover the following skills:
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 strategies to determine the surface area and volume of selected prisms, pyramids, and cylinders.
Connections to the Grade 6 Focal Points (NCTM)
Measurement and Geometry: Problems that involve areas and volumes, calling on students to find areas or volumes from lengths or to find lengths from volumes or areas and lengths, are especially appropriate. These problems extend the students' work in grade 5 on area and volume and provide a context for applying new work with equations.