Geometry: Transversals and Angle Relationships

Study Notes

Transversals

A transversal is a line that intersects two or more other lines.
The lines intersected by the transversal do not necessarily have to be parallel.
When a transversal crosses two lines, it forms special angle pairs: corresponding, alternate, and cointerior angles.

Identifying Parallel Lines

Parallel lines are indicated by using the same arrow set on each line. For example, if AB is parallel to CD, this is written as AB || CD.

Angle Relationships with Parallel Lines

Corresponding Angles are equal when the transversal crosses two parallel lines.
Alternate Angles are equal when the transversal crosses two parallel lines.
Cointerior Angles are supplementary (add up to 180 degrees) when the transversal crosses two parallel lines.

Adjacent Angles

Adjacent angles share a common vertex and arm.
Two adjacent angles on a straight line are supplementary.

Angles in a Revolution

Angles in a complete circle (revolution) add up to 360 degrees.

Vertically Opposite Angles

Vertically opposite angles are formed when two lines intersect.
They are equal and share a common vertex, but are situated on opposite sides of the vertex.

Perpendicular Lines

Perpendicular lines intersect at a right angle (90 degrees).
This is written as AB ⊥ CD, indicating line AB is perpendicular to line CD.

Transversals

A transversal is a line that intersects two or more lines.
The lines intersected by a transversal don’t have to be parallel.

Angle Pairs

A transversal creates special angle pairs.
Corresponding angles: In the same position relative to the transversal and the two intersected lines.
Alternate angles: On opposite sides of the transversal and inside the two intersected lines.
Cointerior angles: On the same side of the transversal and inside the two intersected lines.
Parallel lines, indicated with the same arrow set (e.g., AB||CD), have specific angle relationships when intersected by a transversal.
Corresponding angles are equal.
Alternate angles are equal.
Cointerior angles are supplementary (add up to 180 degrees).

Other Angle Types

Adjacent angles: They share a vertex and one arm, and sit side by side.
Two adjacent angles on a straight line are supplementary: They add up to 180 degrees.
Angles in a revolution: Add up to 360 degrees.
Vertically opposite angles: Form when two lines intersect. They are equal and sit opposite each other across their common vertex.
Perpendicular lines (ab ⊥ cd): Meet at a right angle (90 degrees).

Description

This quiz covers transversals and their relationships with parallel lines, including various types of angles formed when a transversal intersects lines. Learn about corresponding, alternate, and cointerior angles, as well as parallel line indicators and adjacent angles. Test your understanding of these geometric concepts and improve your skills in angle relationships.