12-2 Chords and Arcs
Objectives
To use congruent chords, arcs, and central angles
To use perpendicular bisectors to chords
Dynamic Activity
Chords and Arcs
Lesson Vocabulary
- chord
In the Solve It, you found the length of a chord, which is a segment whose endpoints are on a circle. The diagram shows the chord
Essential Understanding You can use information about congruent parts of a circle (or congruent circles) to find information about other parts of the circle (or circles).
The following theorems and their converses confirm that if you know that chords, arcs, or central angles in a circle are congruent, then you know the other two parts are congruent.
Take Note Theorem 12-4: and Its Converse
Theorem
Within a circle or in congruent circles, congruent central angles have congruent arcs.
Converse
Within a circle or in congruent circles, congruent arcs have congruent central angles.
If
If
You will prove Theorem 12-4 and its converse in Exercises 19 and 35.
Table of Contents
- 6-1 The Polygon Angle-Sum Theorems
- 6-2 Properties of Parallelograms
- 6-3 Proving That a Quadrilateral Is a Parallelogram
- 6-4 Properties of Rhombuses, Rectangles, and Squares
- 6-5 Conditions for Rhombuses, Rectangles, and Squares
- 6-6 Trapezoids and Kites
- 6-7 Polygons in the Coordinate Plane
- 6-8 and 6-9 Coordinate Geometry and Coordinate Proofs