Finding Arc Measures

University:
High School
Course:
High School Mathematics
Academic year:

2022
Views:

231

Pages:

3
Author:

3dy0s3lincd53

Finding Arc Measures Vocabulary Definitions Central Angle: Angles that originate from the center of a circle. Minor Arc: The shortest distance between two points on a circle. Central angle measurement = mAB = (mAB/360°) * (2πr) Major Arc: Longest distance between two points on a circle. Usually indicated with a middle third point. Central angle measurement = mACB = (mACB/360°) * (2πr) Semicircle: Half of the circle. Created by the diameter. = 180° Adjacent Arcs: Two arcs that share a common endpoint. Congruent Circles: Circles with congruent radii. Congruent Arcs: Arcs with the same measures and from the same circle. Or from congruent circles. Similar Arcs: Arcs with the same central angle measurement. Postulates Postulate 10.1 Arc Addition Postulate The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs. mAB + mBC = mABC Theorems Theorem 10.3 Congruent Circles Theorem Two circles are congruent circles if and only if they have the same radius. OA = OB if and only if AC = BD Theorem 10.4 Congruent Central Angles Theorem In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding central angles are congruent. BC ≅ DE if and only if ∠BAC ≅ ∠DAE Theorem 10.5 Similar Circles Theorem All circles are similar. Since Similar means... Same shape Same angles (360°)