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 ARCIf Arc AB = 80o

Then m<C=40o

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 207 16-18

Quadrilateral inside a Circle◦If a quadrilateral is inside of a circle, then the

opposite angles sum to 180 (they are supplementary).