Unit 7

Unit 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 Formulas The 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.

Examples What 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?

Examples If 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?

Examples Circle the figures that are polygons. If the figure is not a polygon, give a justification.

Examples Determine if the polygons below are convex or concave. Circle the convex polygons.

Examples Match the name of the polygon with its representative figure. E F A C B G D

Examples Is there more than one way to name a polygon? Explain the procedure for naming polygons. Give an example and a non-example

Examples Give a congruence statement that would have to be true if the figure above was a regular hexagon.

Unit 7: Properties of Two Dimensional Figures

Theorems If a line is perpendicular to a radius of a circle at a point on the circle, then the line is tangent to the circle.

Theorems If two segments are tangent to a circle from the same external point, then the segments are congruent.

Theorems If a radius (or diameter) is perpendicular to a chord, then it bisects the chord.

Theorems If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.

Postulates The 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 Circles Vertex of the Angle Measure of the Angle Diagrams On a Circle Half 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.