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Geometry 14.2: Chord Length and Arc Measures 14.2 The Inscribed Angle Theorem Background vocabulary: Ø Radius Ø Diameter Ø Arc (major and minor) Ø Central Angle Ø Chord Definition: Inscribed Angle An angle whose vertex is on the circle and each side of the angle intersects the circle at two(2) distinct points. B A C Inscribed Angle Theorem: m = 1/2 m arc it intersects B 700 350 C A SemiCircle Theorem: An angle inscribed in a semicircle is a right angle. SameArc Theorem: In a circle, if two inscribed angles intercept the same arc, then the two(2) angles are congruent. Whats true about ≮A & ≮B? A D B C 1. 2. U V 1120 1 340 m arcUV= m≮1= 3. 3 1120 m≮3= 4. 920 580 1000 E m arcEF= F Q 5. P Find the m≮R: 2n0 1803n0 Justify your answer! n0 T S R 6. The three angles of have measures 40, 60, and 80. If the circle through ABC is drawn, what are the measures of the three minor arcs formed by the points. 7. ABCDEF is a regular hexagon. Find m≮BFE: 7. A B F C E D Find m≮BFE= Review: A 1. Name the central angle?_________________ Radius 2. Segment BC is a ?______________________ Central minor arc. angle is = to the degree of its ___________ 3. The degree measure of the ______________ C B Congruent Circles: radii 4. Two circles are congruent when their ______________ are congruent. 5. Theorem: If two arcs have the same measure, they are congruent and their chords are congruent. 6. Theorem: If two chords have the same length, their minor arcs have the same measure. 7. Draw a picture of both of these theorems and label pieces that make these true. 4. Theorem: If two arcs have the same measure, they are congruent and their chords are congruent. 5. Theorem: If two chords have the same length, their minor arcs have the same measure. 6. Draw a picture of both of these theorems and label pieces that make these true. Are the measures of arcs AB congruent below for the two circles below? Why/why not? 8. A A 8 4 c 60 B o c 60o B Label a major and minor arc. 9. A B 4 D C 12 AD= BC= AB=

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