Question

What does it mean when two lines are parallel?

Answer 1

Hint: Parallel lines are equidistant lines (lines having equal distance from each other) that will never meet. When the graphs of two linear equations are parallel in coordinate geometry, the two equations do not share a solution.The slopes of two parallel lines are equal in coordinate geometry.

Complete step-by-step answer:
These are some examples of parallel lines in different directions: horizontally, diagonally, and vertically.

Transversal to two parallel lines is represented as:

Here the dotted line represents the transversal .
Properties of parallel lines:
When a transversal line cuts a pair of parallel lines, different pairs of angles are formed. These different types of angles are used to prove whether two lines are parallel to each other.
When a transversal line cuts two lines, the properties below will help us determine whether the lines are parallel.
1. Two lines cut by a transversal line are parallel when the corresponding angles are equal.
2. Two lines cut by a transversal line are parallel when the alternate interior angles are equal.
3. Two lines cut by a transversal line are parallel when the alternate exterior angles are equal.
4. Two lines cut by a transversal line are parallel when the sum of the consecutive interior angles is \[{180^ \circ }\].
5. Two lines cut by a transversal line are parallel when the sum of the consecutive exterior angles is \[{180^ \circ }\].

Note: Parallel lines are equidistant lines (lines having equal distance from each other) that will never meet. When the graphs of two linear equations are parallel in coordinate geometry, the two equations do not share a solution.