Geometry Chapter 10: Circles - Notes 10.2
This section focuses on arcs and their measurements, as well as the relationships between arcs and central angles.
The page begins by defining the measures of different types of arcs:
- Minor arc: Measure is between 0° and 180°
- Major arc: Measure is 360° minus the measure of the corresponding minor arc
- Semicircle: Measure is always 180°
Highlight: The measure of a major arc is between 180° and 360°.
The concept of adjacent arcs and arc addition is explained and illustrated with an example.
Example: mAB + mBC = mAC, where AB and BC are adjacent arcs.
A series of examples is provided to practice finding arc measures in a circle, including minor arcs, major arcs, and semicircles.
The page introduces an important theorem relating diameters or radii to chords:
Definition: If a diameter or radius is perpendicular to a chord, then it bisects the chord and its arc.
The concept of congruent arcs is also explained and illustrated.
Vocabulary: Arcs are considered congruent if they have the same measure and are in the same or congruent circles.
The section concludes with practice problems involving concentric circles and chord measurements.