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Allie Buksha 6-9-09 Geometry Mr. Chester. Circle Proofs. VOCABULARY. RADIUS - a line segment drawn from the center point to a point on the circle DIAMETER – a line segment from one point on the circle to another, and passes the center point
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Allie Buksha 6-9-09 Geometry Mr. Chester Circle Proofs
VOCABULARY • RADIUS- a line segment drawn from the center point to a point on the circle • DIAMETER – a line segment from one point on the circle to another, and passes the center point • SECANT – a line segment drawn from an external point to a point on the circle while passing through the circle once. • TANGENT– a line segment drawn from an external point to a point on the circle, and it extended wont intersect the circle again • CHORD – a line from one point on the circle to another
TYPES OF ANGLES • INSCRIBED ANGLES – an angle formed by two chords with the vertex on the circle • CENTRAL ANGLES – an angle formed by two radii with the vertex on the circle
THEOREOMS • All radii of a circle are congruent • In a circle, congruent central angles have congruent arcs • In a circle, congruent arcs have congruent chords and vice versa • A diameter perpendicular to a chord bisect the chord and its arcs • Congruent chords in the same circle are equidistant from the center of the circle • In a circle, if two chords are unequal, the shorter chord is farther from the center • An angle inscribed in a semicircle is a right angle • In a circle, inscribed angles that intercept the same arc are congruent • Parallel lines intercept congruent arcs • If a line is tangent to a circle then it is perpendicular to the radius at that point • Two tangent segments drawn to a circle from an external point are congruent
