Math - 2018-19
G.10 - Angles of Polygons
G.10 The student will solve problems, including practical problems, involving angles of convex polygons. This will include determining the
a) sum of the interior and/or exterior angles;
b) measure of an interior and/or exterior angle;
c) number of sides of a regular polygon.
- I can create a home plate marker for softball field, exert
enough force on a bolt to tighten it, and determine how many carpet squares to
cover a gazebo floor.
- I will be
able to figure out the sum
of interior angles when I know the number of sides of a polygon, and with that
knowledge find missing interior angle measurements.
UNDERSTANDING THE STANDARD
· In convex polygons, each interior angle has a measure less than 180°.
· In concave polygons, one or more interior angles have a measure greater than 180°.
· Two intersecting lines form angles with specific relationships.
· An exterior angle is formed by extending a side of a polygon.
· The exterior angle and the corresponding interior angle form a linear pair.
· The sum of the measures of the interior angles of a convex polygon may be found by dividing the interior of the polygon into nonoverlapping triangles.
· Both regular and nonregular polygons can tessellate the plane.
· A regular polygon will tessellate the plane if the measure of an interior angle is a factor of 360.
· The sum of the measures of the angles around a point in a tessellation is 360°.· Tessellations can be found in art, construction and nature.
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
· G.10abc1 Solve
problems, including practical problems, involving angles of convex polygons.
· G.10a1 Determine
the sum of the measures of the interior and exterior angles of a convex
· G.10b1 Determine
the measure of each interior and exterior angle of a regular polygon.
· G.10c1 Determine
the number of sides of a regular polygon, given the measures of interior or exterior
angles of the polygon.
· G.10b2 Determine angle measures of a regular polygon in a tessellation.
polygon, measure, interior angle, exterior angle, tessellation/tessellate, sum,
convex polygon, regular, regular polygon, side, irregular/nonregular polygon,
factor, plane, intersecting lines, corresponding interior angle, linear pair,
uniform tessellation, semi-regular tessellation, regular tessellation, divide,