Parallel Lines and Circles

Previously Introduced

Line: A line has only one dimension: length. It continues forever in two directions (so it has infinite length), but it has no width at all. A line connects two points via the shortest path, and then continues on in both directions.

Plane: A plane is a flat, two-dimensional object. We often represent a plane by a piece of paper, a blackboard, or the top of a desk. In fact, none of these is actually a plane, because a plane must continue infinitely in all directions and have no thickness at all. A plane can be defined by two intersecting lines or by three non-collinear points.

Point: A point specifies only location; it has no length, width, or depth. We usually represent a point with a dot on paper, but the dot we make has some dimension, while a true point has dimension 0.

Quadrilateral: A quadrilateral is a polygon with exactly four sides.

Ray: A ray can be thought of as a half a line. It has a point on one end, and it extends infinitely in the other direction.

Vertex: A vertex is the point where two sides of a polygon meet.

New in This Session

Central Angle: A central angle is an angle with its vertex at the center of a circle.

Circle: A circle is the set of all points in a plane that are equidistant from a given point in the plane, which is the center of the circle.

Diameter: A circle’s diameter is a segment that passes through the center and has its endpoints on the circle.

Inscribed Angle: An inscribed angle is an angle whose vertex is on a circle and whose rays intersect the circle.

Parallel Lines: Parallel lines are two lines in the same plane that never intersect. Another way to think about parallel lines is that they are “everywhere equidistant.” No matter where you measure, the perpendicular distance between two parallel lines is constant.

Radius: The radius of a circle is the distance from the circle’s center to a point on the circle, and is constant for a given circle.

Transversal: A transversal is a line that passes through (transverses) two other lines. We often consider what happens when the two other lines are parallel to each other.

Note 1

Materials Needed: 

Many of the activities in this session are built around the use of a dynamic geometry construction software package called Geometer’s Sketchpad. Your school may already have a copy or own similar software, or you can download a free trial version from Key Curriculum Press. Go to http://www.keypress.com/sketchpad/ and download the Instructor’s Evaluation Edition.

Optional

• Two pieces of paper
• Overhead projector
• Two transparencies