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Study for Test 3 – Chapters 6,7 – Geometry MATH 0470 – David Hubbard 6. Circles 6.1. Circles and related segments and angles – know circles, central angles, inscribed angles, arcs, sum of arcs in a circle = 360, and arc addition. 6.2. More angle measures in the circle – know tangents, secants, inscribed and circumscribed circles/polygons. Understand and be able to use all angle/arc relationships for table 6.2 (page 261-2). Most of these formulas will be provided. 6.3. Line and segment relationships in the circle - Understand and be able to use all segment relationships for table 6.2 (page 261-2). Formulas provided with the test. 6.4. Inequalities for the circle – Know the table (from slides) with relationships between arcs, chords, central angles, and distance from chord to the center. 6.5. Locus of points 6.5.1. bisector – points equidistant from endpoints of a segment 6.5.2. bisector – points equidistant from sides of an angle 6.5.3. parallel line – points a fixed distance from a line 6.5.4. parallel plane – points a fixed distance from a plane 6.5.5. circle – points a fixed distance away from a point (center) 6.6. Concurrence of lines – lines intersect at a common point. 6.6.1. altitudes, bisectors, and bisectors of a triangle are concurrent 6.6.2. medians of a triangle are concurrent and intersect at a point that is 2/3 the distance from any vertex to the midpoint of the opposite side. 7. Areas of Polygons and Circles 7.1. Area and initial postulates – area addition 7.1.1. Square – A s 2 7.1.2. Rectangle – A l w 7.1.3. Parallelogram – A b h 7.1.4. Trapezoid – A = ½(b1+b2)h 7.1.5. Triangle – A = ½(bh) 7.2. Perimeter and area of polygons 7.2.1. Quadrilateral – P = a+b+c+d, Triangle – P = a+b+c 7.2.2. Rectangle – P = 2b+2h, Parallelogram – P = 2b+2s 7.2.3. Square/rhombus – P = 4s 7.2.4. Heron’s formula - A s(s a)( s b)( s c) , s 1 / 2(a b c) 7.3. Regular polygons and area – know radius of a polygon, the apothem, and the central angle of a polygon 7.3.1. Central angle – C = (360)/n 7.3.2. Area of a regular polygon – A = ½(aP) 7.4. Circumference and area of a circle m ( 2 r ) 7.4.1. C = d, or C = 2r, length of an arc - l 360 7.4.2. A = r2 7.5. More area relationships in the circle m r 2 , Asegment Asec tor A 7.5.1. Asector = 360 7.5.2. Area of triangle with inscribed circle = ½(rP)