Properties of Parallel Lines
Proposition Properties of Parallel Lines
If two lines are parallel and intersected by a transversal, then:
- Corresponding angles are equal.
- Alternate angles are equal.
- Co-interior angles are supplementary (their measures sum to \(180^\circ\)).
Example
Calculate the measure of the unknown angle \(x^\circ\), given that the lines are parallel.
Since the angles are alternate and the lines are parallel, they are equal.$$\begin{aligned}x^\circ &= 70^\circ \quad (\text{alternate angles are equal})\end{aligned}$$
Proposition Parallel Lines from Equal Angles
If two corresponding angles or two alternate angles formed by the same transversal are equal, then the lines are parallel.
Example
Show that the lines are parallel, given the angle measures.
Since the corresponding angles are equal (\(110^\circ = 110^\circ\)), the lines are parallel.