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Properties of Two Dimensional Figures

Properties of Two Dimensional Figures. Unit 7. Polygons. Unit 7: Properties of Two Dimensional Figures. Polygons and Their Formulas. Polygon. _______________ - A two dimensional figure with these characteristics: It is made of straight line segments.

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Properties of Two Dimensional Figures

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  1. Properties of Two Dimensional Figures Unit 7

  2. Polygons Unit 7: Properties of Two Dimensional Figures

  3. Polygons and Their Formulas Polygon • _______________ - 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.

  4. Polygons and Their Formulas Convex Polygon • _______________ - 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 _______________. Concave Polygon Regular Polygon (n – 2)180

  5. 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 .

  6. 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?

  7. 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?

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

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

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

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

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

  13. Circles and Angles Unit 7: Properties of Two Dimensional Figures

  14. 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.

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

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

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

  18. 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.

  19. Angle Relationships in Circles

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