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LESSON 19.1 CENTRAL ANGLES AND INSCRIBED CIRCLES PLEASE TEAR OUT PAGES 1005-1018 PARTS OF A CIRCLE… • Chord – a segment whose endpoints lie on a circle. • Central Angle – an angle less than 180° whose vertex lies at the center of the circle. • Inscribed Angle – an angle whose vertex lies on a circle and whose sides contain chords of the circle. • Arc – a continuous portion of a circle consisting of two points (called the endpoints of the arc) and all the points on the circle between them. UNDERSTANDING ARCS AND ARC MEASURE FINDING INSCRIBED ANGLE MEASURES… EXAMPLE 1 – IDENTIFY THE FOLLOWING PARTS OF EACH CIRCLE… A) CHORD(S) B) INSCRIBED ANGLE(S) C) CENTRAL ANGLE(S) A) Chords 𝑃𝑇 𝑃𝑅 B) Inscribed Angles ∠𝑇𝑃𝑅 C) Inscribed Angles ∠𝑅𝑄𝑆 EXAMPLE 2 𝑚∠𝑀𝐶𝑁 = 27° − 𝑉𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝐴𝑛𝑔𝑙𝑒𝑠 𝑚∠𝑀𝐶𝑃 = 90° − 𝑆𝑢𝑝𝑝𝑙𝑒𝑚𝑒𝑛𝑡𝑎𝑟𝑦 ∠𝑠 33° 𝑚𝑀𝑃 = 90° 18° 𝑚𝑀𝑃 = 𝑚𝑀𝑁 + 𝑚𝑁𝑃 90° = 27° + 𝑚𝑁𝑃 27° 𝑚𝐵𝐷 = 18° 𝑚∠𝐴𝐶𝐵 = 33° − 𝑉𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝐴𝑛𝑔𝑙𝑒𝑠 𝑚𝐴𝐵 = 33° 𝑚𝐴𝐷 = 33° + 18° = 51° 63° = 𝑚𝑁𝑃 EXAMPLE 3 1 𝑚∠𝐷𝐴𝐸 = 𝑚𝐷𝐸 2 1 54° = 𝑚𝐷𝐸 2 1 𝑚𝐵𝐷 2 𝑚𝐵𝐷 = 𝑚𝐵𝐸 + 𝑚𝐷𝐸 𝑚∠𝐷𝐴𝐵 = 𝑚𝐵𝐷 = 18° + 108° 1 𝑚∠𝐷𝐴𝐵 = (126°) 2 𝑚𝐵𝐷 = 126° 108° = 𝑚𝐷𝐸 1 𝑚∠𝐴𝐷𝐸 = 𝑚𝐴𝐸 2 1 𝑚∠𝐴𝐷𝐸 = (180°) 2 𝑚∠𝐴𝐷𝐸 = 90° 𝑚∠𝐷𝐴𝐵 = 63° EXAMPLE 4 - 1 𝑚∠𝑋𝑍𝑊 = 𝑚𝑊𝑋 2 1 9° = 𝑚𝑊𝑋 2 18° = 𝑚𝑊𝑋 𝑚𝑊𝑍 = 𝑚𝑊𝑋 + 𝑚𝑋𝑍 180° = 18° + 𝑚𝑋𝑍 1 𝑚∠𝑊𝑋𝑍 = 𝑚𝑊𝑍 2 1 𝑚∠𝑊𝑋𝑍 = (180°) 2 162° = 𝑚𝑋𝑍 𝑚∠𝑊𝑋𝑍 = 90° ASSIGNMENT #38 • Pg. 1012 • #1-19 all