Angle and Parallel Lines

When two straight lines cross each other,

and

are pair of vertical angles.

and

are pair of vertical angles.
Vertical angles are equal in size.

Drag the red point to rotate the line arround the center point. You can observe the two angles are always equal.

A line passing through two or more lines in a plane is called a transversal. When a transversal cuts two lines,

and

are corresponding angles.

and

are also corresponding angles.

and

are alternate angles.

and

are also alternate angles.

When a transversal cuts two parallel lines, corresponding angles are equal in size.

Drag the red point. Move the line to place the angle to corresponding angles.

When a transversal cuts two parallel lines, alternate angles are equal in size.

Drag the red point. Rotate the figure to place the angles on the alternate angles.

When a transversal cuts two lines, if corresponding angles are equal in size, or if alternate angles are equal in size, then two lines are parallel.