Lesson 3: 9-3: Arcs and Chords

1. How are chords and their arcs related?
2. What is the relationship between a diameter that is perpendicular to a chord?

G.CO.12
Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.)
G.C.2
Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.
G.MG.3
Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).

The endpoints of a chord are also endpoints of an arc. Two minor arcs are congruent if and only if their corresponding chords are congruent. Two chords are congruent if and only if they are equidistant from the center of the circle.

Embroidery hoops are used in sewing, quilting, and cross-stitching as well as for embroidering. The endpoints of the snowflake shown are both the endpoints of a chord and the endpoints of an arc.

Students approaching grade level can be given practice problems in small groups to work with other students or directly with the teacher.
Students beyond grade level can make deeper connections
by creating circles and labeling vocabulary: diameter, chord, perpendicular bisector, radii, etc.

Formative Assessment

Textbook in class

Access online textbook and resources through class link.