1. Sect. 12-3 Properties of Chords and Arcs Geometry Honors

2. What and Why What? – Find the lengths of chords and measures of arcs of a circle. – Locate the center of a circle using chords. Why? – To find the radius of a circle in real-life situations such as archaeology.

3. Congruent Arcs and Chords

4. Theorem 12-5 In the same circle or in congruent circles, – (1) congruent central angles have congruent arcs; and – (2) congruent arcs have congruent central angles.

5. Theorem 12-6 In the same circle or in congruent circles, – (1) congruent chords have congruent arcs – (2) congruent arcs have congruent chords

6. Theorem 12-7 A diameter that is perpendicular to a chord bisects the chord and its arc.

7. Example

8. Theorem 12-8 The perpendicular bisector of a chord contains the center of the circle.

9. Chords Equidistant from the Center of a Circle Theorem 12-9 – In the same circle or in congruent circles, (1) chords equidistant from the center are congruent (2) congruent chords are equidistant from the center.

11. StatementsReasons 2.Given 3.Given 4. Definition of right angles 5. HL Theorem 6.CPCTC 8.Substitution 9. Multiplication Property of Equality