1 / 13

Polygons

Polygons. Polygons. Definition:. A closed figure formed by a finite number of coplanar segments so that each segment intersects exactly two others, but only at their endpoints. These figures are not polygons. These figures are polygons. Classifications of a Polygon. Convex:.

gil-gallegos
Télécharger la présentation

Polygons

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Polygons Lesson 3-4: Polygons

  2. Polygons Definition: A closed figure formed by a finite number of coplanar segments so that each segment intersects exactly two others, but only at their endpoints. These figures arenot polygons These figures are polygons Lesson 3-4: Polygons

  3. Classifications of a Polygon Convex: No line containing a side of the polygon contains a point in its interior Concave: A polygon for which there is a line containing a side of the polygon and a point in the interior of the polygon. Lesson 3-4: Polygons

  4. Classifications of a Polygon Regular: A convex polygon in which all interior angles have the same measure and all sides are the same length Irregular: Two sides (or two interior angles) are not congruent. Lesson 3-4: Polygons

  5. Polygon Names Triangle 3 sides 4 sides Quadrilateral 5 sides Pentagon 6 sides Hexagon 7 sides Heptagon 8 sides Octagon 9 sides Nonagon 10 sides Decagon Dodecagon 12 sides n sides n-gon Lesson 3-4: Polygons

  6. Convex Polygon Formulas….. Diagonals of a Polygon: A segment connecting nonconsecutive vertices of a polygon For a convex polygon with n sides: The sum of the interior angles is The measure of one interior angle is The sum of the exterior angles is The measure of one exterior angle is Lesson 3-4: Polygons

  7. Examples: • Sum of the measures of the interior angles of a 11-gon is • (n – 2)180°  (11 – 2)180 °  1620 • The measure of an exterior angle of a regular octagon is • The number of sides of regular polygon with exterior angle 72 ° is • The measure of an interior angle of a regular polygon with 30 sides Lesson 3-4: Polygons

  8. TRIANGLE FUNDAMENTALS Triangle Sum Theorem: The sum of the interior angles in a triangle is 180˚

  9. Example: 5. In Δ ABC, m<A = 45°, m<B = 90°, find m<C. m<C= 180°- (45° + 90°) m<C= 45°

  10. Example: 6.If 2x, x and 3x are the measures of the angles of a triangle, find the angles. 2x+x+3x=180° 6x= 180° x=30° Angles are 90°, 30° and 60°

  11. Exterior Angle Theorem The measure of the exterior angle of a triangle is equal to the sum of the measures of the remote interior angles. Remote Interior Angles Exterior Angle

  12. Example 7: Find the mA. 3x - 22 = x + 80 3x – x = 80 + 22 2x = 102 X=51 m<A=51°

  13. Corollaries: 1.If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent. 2. Each angle in an equiangular triangle is 60˚ 3. Acute angles in a right triangle are complementary. 4. There can be at most one right or obtuse angle in a triangle.

More Related