Lesson: Parallel Chords and Tangents in a Circle Mathematics

In this lesson, we will learn how to use the parallel chords and the parallel tangents and chords of a circle to deduce the equal measures of the arcs between them and find missing lengths or angles.

Lesson Plan

Students will be able to

understand that the measures of the arcs between parallel chords of a circle are equal,
understand that the measures of the arcs between a chord and a parallel tangent of a circle are equal,
understand that if the measures of the arcs between two chords (or between a chord and a tangent) are equal, we can deduce that the lines must be parallel,
use theories of parallel chords and parallel chords and tangents to find unknown angles and lengths.

Lesson Presentation

Lesson Video

Lesson Explainer

Lesson Worksheet

Q1:

Consider the two arcs of a circle between any two parallel chords. Are these arcs equal in both length and measure?

Q2:

True or False: Assume that the two arcs, and , have the same length; and the two chords, and , are parallel. Then, the length of chord equals the length of chord .

Q3:

In the given figure, the measure of , the measure of , and the measure of . What can we conclude about and ?