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Relationships Between Lines and Planes
 When two lines lie in the same plane and do not intersect, they are parallel to each other.
Two lines that intersect each other and form 90 degree angles are perpendicular to each other.
Lines that do not lie in the same plane and do not intersect are skew lines.
Similarly, if two planes do not intersect each other, they are parallel planes. In the diagram, the top and bottom of the cube represent parallel planes.
Angle Relationships
A line that intersects two or more other lines in a plane is called a transversal. Two lines and a transversal form eight angles. Some pairs of the angles have special relationships.
Corresponding Angles
When two lines are intersected by a transversal, a pair of angles that lie on the same side of the transversal and on the same sides of the other two lines are called corresponding angles. If the lines are parallel, then the corresponding angles are congruent.
In this diagram, angles 4 and 8 are corresponding angles.
 Alternate Interior Angles
When two lines are intersected by a transversal, a pair of nonadjacent angles that lie on opposite sides of the transversal and between the other two lines are called alternate interior angles. If the lines are parallel, then the alternate interior angles are congruent.
In this diagram, angles 4 and 5 are alternate interior angles.
 Alternate Exterior Angles
When two lines are intersected by a transversal, a pair of angles that line on opposite sides of the transversal and outside the other two lines are called alternate exterior angles. If the lines are parallel, then the alternate exterior angles are congruent.
In this diagram, angles 2 and 7 are alternate exterior angles.
 Same-Side Interior Angles
When two lines are intersected by a transversal, a pair of angles that lie on the same side of the transversal and between the two lines are called same-side interior angles. If the lines are parallel, then the angles are supplementary.
In this diagram, angles 4 and 6 are same-side interior angles.
Find the measure of each angle formed by parallel lines and a...
Find the measure of each angle formed by parallel lines and a transversal. Use angle relationships to create algebraic equations.
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