Download Lesson 19.1 central angles and inscribed circles

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