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  Major Arcs contain 3 letters and are > 180 degrees  Semicircles = 180 degrees

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

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

ANGLE = ½ ARC If Arc AB = 80 o Then m<C=40 o 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

Practice page Quadrilateral inside a Circle ◦If a quadrilateral is inside of a circle, then the opposite angles sum to 180 (they are supplementary).