Lessons

1. Basics
2. Deductive Reasoning
3 - Parallel lines
4 - Congruent Triangles
6 - Inequalities
7 - Similar Polygon
8 - Rt. Triangles
9 - Circles
10 - Constructions
11 - Areas of 2D objects
12 - Areas and Volumes
13 - Coordinates

Arcs and Chords

Objective:

• Learning about the basics of arcs and chords

Lesson 9-2 Arcs and Chords:

Central angle: An angle with its vertex at the center of the circle

Minor Arc: The measure of a circle's central angle

Major Arc: The number found by subtracting the measure of the minor arc from 360.

Arc AB is a minor arc and Arc ACB is a major arc

Semicircles: The two arcs of a circle that are cut off by a diameter. The measure of a semicircle is 180.

Arc AB is a semicircle

Congruent Arcs: Arcs that are in the same or congruent circles that have equal measures

 Postulate 16 Arc Addition Postulate The measure of the arc formed by two adjacent arcs is the sum of the measures of these two arcs. Arc AB + Arc BC = Arc ABC   Theorem 9-3 In the same circle or in congruent circles, two minor arcs are congruent if and only if their central angles are congruent.   Theorem 9-4 In the same circle or in congruent circles: (1) Congruent arcs have congruent chords (2) Congruent chords have congruent arcs Chord AD is congruent to chord BC, therefore Arc AD is congruent to Arc BC   Theorem 9-5 A diameter that is perpendicular to a chord bisects the chord and its arc Chord AB is congruent to chord BC and Arc AD is congruent to Arc DC   Theorem 9-6 In the same circle or in congruent circles:(1) Chords equally distant from the center (or centers) are congruent. (2) Congruent chords are equally distant from the center (or centers).

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