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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 = 2r, 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)