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6.3 – 6.4 Properties of Chords and Inscribed Angles

6.3 – 6.4 Properties of Chords and Inscribed Angles. Theorem Review: Two tangents from the same point are congruent Tangents are perpendicular (form a 90 degree angle) with the radius A central angle has the same measure as its arc Minor Arcs contain 2 letters and are < 180 degrees

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6.3 – 6.4 Properties of Chords and Inscribed Angles

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  1. 6.3 – 6.4 Properties of Chords and Inscribed Angles

  2. Theorem Review: • Two tangents from the same point are congruent • Tangents are perpendicular (form a 90 degree angle) with the radius • A central angle has the same measure as its arc • Minor Arcs contain 2 letters and are < 180 degrees • Major Arcs contain 3 letters and are > 180 degrees • Semicircles = 180 degrees

  3. Chord Properties: • If two arcs are congruent then the corresponding chords are congruent .

  4. Chord Properties continued… • If one chord is a perpendicular bisector of another chord, then the first chord is the diameter • If a diameter is perpendicular to a chord, then the diameter bisects the chord and its arc. • See “cat” drawing

  5. Inscribed Angles • An inscribed angle is an angle whose vertex is ON THE CIRCLE • This is different from a central angle whose vertex is ON THE CENTER OF THE CIRCLE ANGLE = ½ ARCIf Arc AB = 80o Then m<C=40o

  6. Quadrilateral inside a Circle • If a quadrilateral is inside of a circle, then the opposite angles sum to 180 (they are supplementary). Practice page 207 16-18

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