GEOMETRY FUNDAMENTALS UNIT 11 Essays - Geometry, Mathematics, Space

GEOMETRY FUNDAMENTALS UNIT 11 REVIEW CIRCLES Center of an arcThe center of the circle that contains the arc.Central angleAn angle in the plane of a circle whose vertex is at the center of the circle.ChordA segment whose endpoints are on the circle.CircleThe set of all points in a plane that are the same distance from a given point in that plane called its center.Concentric circlesTwo or more circles that lie in the same plane and have the same center.Congruent circlesCircles that have equal radii.DiameterA segment passing through the center with endpoints on the circle.Inscribed angleAn angle whose sides contain the endpoints of an arc and whose vertex is a point of the arc other than an endpoint of the arc.Major arcThe union of two points of the circle (not endpoints of a diameter) and all points of the circle that are in the exterior of the central angle whose sides contain the two points.Midpoint of an arcA point x on arc AB such that m = m .Minor arcThe union of two points of the circle (not endpoints of a dia meter) and all points of the circle that are in the interior of the central angle whose sides contain the two points.RadiusA segment whose endpoints are the center of a circle and a point on the circle.SecantA line that contains a chord.SemicircleThe union of the endpoints of a diameter and all points of the circle that are on the same side of the diameter.SphereThe set of all points that are the same distance from a given point.Tangent lineA line in the plane of a circle that intersects the circle in exactly one point. P16: If the intersection of and of a circle is the single point B , then m + m = m . (Arc addition) 6-1: A radius drawn to a point of tangency is perpendicular to the tangent. 6-2: A line in the plane of a circle and perpendicular to a radius at its outer endpoint is tangent to the circle. 6-3: If in the same circle or congruent circles two central angles are equal, then their arcs are equal. 6-4: If in the same circle or congruent circles two minor arcs are equal, then their central angles are equal. 6-5: If in the same circle or congruent circles the chords are equal, then the arcs are equal. 6-6: If in the same circle or in congruent circles the arcs are equal, then the chords are equal. 6-7: If a diameter is perpendicular to a chord, then it bisects the chord and its two arcs. 6-8: If in the same circle or congruent circles the chords are equidistant from the center, then their lengths are equal. 6-9: If in the same circle or congruent circles the chords have the same length, then they are equidistant from the center. MORE THEOREMS 6-10: The measure of an inscribed angle is equal to half the measure of its intercepted arc Corollary 1: An angle inscribed in a semicircle is a right angle. Corollary 2: The opposite angles of an inscribed quadrilateral are supplementary. Corollary 3: If two angles intercept the same or equal arcs, then the angles are equal. 6-11: The measure of an angle formed by a secant ray and a tangent ray drawn from a point on a circle is equal to half the measure of the intercepted arc. 6-12: The measure of an angle formed by two secants that intersect inside the circle is equal to half the sum of the intercepted arcs. 6-13: The measure of the angle formed by two secants intersecting outside the circle is equal to half the difference of the intercepted arcs. 6-14: The measure of the angle formed by a tangent ray and a secant ray intersecting outside the circle is equal to half the difference of the intercepted arcs. 6-15: The measure of the angle formed by two tangent rays intersecting outside the circle is equal to half the difference of the intercepted arcs. 6-16: If two chords intersect in a circle, then the product of the lengths of the segments of one chord is equal to the product of the length of the segments of the other chord. 6-17: If two