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.