Table of Contents
Explain in Detail: Condition for Parallel Lines
Parallel lines are lines that are in the same plane and have the same direction. They never intersect, and their distance apart is constant.
Properties of Parallel Lines
- Parallel lines have the same slope.
- Parallel lines never intersect.
- The distance between parallel lines is always the same.
Transversal
- A transversal is a line that intersects two other lines.
- A transversal line is a line that intersects two or more other lines at different angles. A transversal can be used to determine the angles between two lines, or the measure of a specific angle. In the diagram below, line AB is the transversal, and lines AC and BD are the other lines that it intersects.
- Angles A and C are both right angles, because they are both 90 degrees. Angle B is not a right angle, because it is not 90 degrees. The measure of Angle A is 90 degrees, because it is the angle formed by the intersection of two perpendicular lines. The measure of Angle C is also 90 degrees, because it is the angle formed by the intersection of two parallel lines.
Corresponding Angles
The angles below are corresponding angles.
- Angle 1 and Angle 3 are corresponding angles because they are both angles formed by a line and a transversal intersecting two lines.
- Angle 2 and Angle 4 are also corresponding angles because they are both angles formed by a line and a transversal intersecting two lines.
- In geometry, two angles are called corresponding angles if they have the same measure. Corresponding angles are always adjacent angles. For example, in the image below, angles A and C are corresponding angles because they have the same measure, 90 degrees.
Alternate Interior Angles
- An angle that is not a right angle is called an alternate interior angle.
- The measure of an alternate interior angle is always less than the measure of a right angle.
- In geometry, alternate interior angles are two angles that are in between two parallel lines and are next to each other. The angles are opposite each other and are formed by two lines that are parallel to each other. The two angles are also equal in measure.
