# Congruent Chords Conjecture

### Explanation:

A **chord** is a line segment with endpoints on the circle. We want to know when two chords in a circle are congruent. This conjecture tells us that the central angles determined by the congruent chords are equal in measure, which implies that the **intercepted arcs** are congruent. This conjectures also tells us that the distances from the center of the circle to two congruent chords are equal.

### The precise statement of the conjecture is:

**Conjecture (***Congruent Chords* ):

If two chords of a circle are congruent, then they determine central angles which are equal in measure.

If two chords of a circle are congruent, then their intercepted arcs are congruent.

Two congruent chords in a circle are equal in distance from the center.

### Interactive Sketch Pad Demonstration:

### Linked Activity:

Please feel free to try the activity sheet associated with this conjecture.

**Next:** Perpendicular Bisector of a Chord

**Previous:** Rectangle Conjectures

**Back:** Conjectures in Geometry Conjecture List or to the Introduction.