- Students will define a tangent and recognize that a tangent is perpendicular to the radius of the circle at the point of tangency.
- Students will understand that two segments tangent to a circle from a common point outside the circle are congruent.
- Students will be able to prove that the tangent segments from an external common point are congruent.
- secant line
- tangent line
- point of tangency
- tangent segments
About the Lesson
This lesson involves students looking at tangents and their properties. As a result students will:
- Manipulate a point on a line to visualize when it is a secant line and when it becomes a tangent line to the circle.
- Using a constructed tangent line, describe the relationships of a tangent line to a radius at the point of tangency.
- Using two tangent lines intersecting outside a circle, discover the relationships of tangent segments.
- Step through and justify a proof for tangent segments.