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Properties of Congruent Arcs and Chords in Circles

This document outlines key theorems related to congruent arcs and chords in circles. Theorem 9-4 states that congruent arcs have congruent chords and vice versa. Theorem 9-5 establishes that a diameter perpendicular to a chord bisects both the chord and its associated arc. Theorem 9-6 explains that in the same or congruent circles, chords that are equally distant from the center are congruent, and that congruent chords are also equally distant from the center. Various examples illustrate these concepts.

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Properties of Congruent Arcs and Chords in Circles

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  1. Theorem 9-4 • In the same circle (or congruent circles) • Congruent arcs have congruent chords. • Congruent chords have congruent arcs.

  2. If arc AB is congruent to arc BC, then segment AB is congruent to segment BC The converse is true also… Example A B C D

  3. Theorem 9-5 • A diameter that is perpendicular to a chord bisects the chord and its arc.

  4. If CD is perpendicular to AB, then AZ is cong to BZ Arc AD is cong to Arc BD Example A D Z B C

  5. Given: EF=10 AZ=5 Find ZB Find arc DB Try this one… A D E Z B C F

  6. Theorem 9-6 • In the same circle (or in congruent circles) • Chords equally distant from the center are congruent. • Congruent chords are equally distant from the center.

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