Post on 17-Dec-2015
Properties of Two Dimensional Figures
Unit 7
PolygonsUnit 7: Properties of Two Dimensional Figures
Polygons and Their Formulas_______________ - A two dimensional figure
with these characteristics:It is made of straight line segments.Each segment touches exactly two other
segments at their endpoints.It is closed. This means that it divides the
plane into two distinct regions, one inside and the other outside the polygon.
Polygon
Polygons and Their Formulas_______________ - A polygon in which all
interior angles measure less than 180˚._______________ - A polygon with at least one
interior angle that measures more than 180˚._______________ - A polygon in which all sides
and interior angles are congruent.In convex polygons, the sum of the interior
angles is _______________.
Convex Polygon
Concave Polygon
Regular Polygon
(n – 2)180
Polygons and Their FormulasThe measure of each interior angle of a
regular polygon is .In convex polygons, the sum of the exterior
angles is .The measure of each exterior angle of a
regular polygon is .
ExamplesWhat is the interior angle sum of a hexagon?
What is the measure of an exterior angle of a regular heptagon?
What is the measure of an interior angle of a regular decagon?
ExamplesIf a regular polygon has an interior angle sum
of 1980˚, how many sides does the polygon have?
If the measure of an exterior angle of a regular polygon is 45˚, haw many sides does the polygon have? What is the measure of the interior angle?
ExamplesCircle the figures that are polygons. If the
figure is not a polygon, give a justification.
ExamplesDetermine if the polygons below are convex
or concave. Circle the convex polygons.
ExamplesMatch the name of the polygon with its
representative figure.EF
A
C
B
G
D
ExamplesIs there more than one way to name a
polygon? Explain the procedure for naming polygons. Give an example and a non-example
ExamplesGive a congruence statement that would have
to be true if the figure above was a regular hexagon.
Circles and AnglesUnit 7: Properties of Two Dimensional Figures
TheoremsIf a line is perpendicular to a radius of a
circle at a point on the circle, then the line is tangent to the circle.
TheoremsIf two segments are tangent to a circle from
the same external point, then the segments are congruent.
TheoremsIf a radius (or diameter) is perpendicular to a
chord, then it bisects the chord.
TheoremsIf a quadrilateral is inscribed in a circle, then
its opposite angles are supplementary.
PostulatesThe measure of a minor arc is equal to the
measure of its central angle.
The measure of a major arc is equal to 360˚ minus the measure of its central angle.
Angle Relationships in CirclesVertex of the
AngleMeasure of the
AngleDiagrams
On a CircleHalf the
measure of its intercepted arc.
Inside a Circle
Half the sum of the measures of its intercepted
arc.
Outside a Circle
Half the difference of the measures of its
intercepted arcs.