Parallel Lines and Shapes
Definition of Parallel Lines
Parallel lines are two or more lines that are always the same distance apart and never meet. They have the same slope and will never intersect, no matter how far they are extended.
Symbol for Parallel Lines
The symbol for parallel lines is "||". If two lines are parallel, we can write it as line AB || line CD.
Properties of Parallel Lines
Here are some key properties of parallel lines:
- Parallel lines have the same slope.
- Corresponding angles formed by a transversal (a line that intersects two or more lines) are congruent.
- Alternate interior angles and alternate exterior angles are congruent.
- Consecutive interior angles are supplementary, meaning they add up to 180 degrees.
Parallel Shapes
In geometry, we often encounter parallel lines in the context of parallel shapes such as parallelograms and trapezoids.
Parallelograms
A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length. The opposite angles of a parallelogram are also equal.
Trapezoids
A trapezoid is a quadrilateral with one pair of parallel sides. The parallel sides are called the bases of the trapezoid.
Study Guide
When studying parallel lines and shapes, it's important to understand the following concepts:
- Definition of parallel lines and the symbol used to denote parallel lines.
- Properties of parallel lines, including the relationships between angles formed by a transversal.
- Identifying and working with parallel shapes such as parallelograms and trapezoids.
- Solving problems involving parallel lines and shapes, including finding missing angles and side lengths.
◂Math Worksheets and Study Guides Eighth Grade. Rational numbers and operations
Worksheet/Answer key
Worksheet/Answer key
Worksheet/Answer key