1 / 14

Section 8.1: Find Angle Measures in Polygons

Section 8.1: Find Angle Measures in Polygons. Polygon. DEFINITION: closed plane figure formed by 3 or more line segments such that each segment intersects exactly 2 other segments only at endpoints. These figures are not polygons. These figures are polygons. Vertex.

komala
Download Presentation

Section 8.1: Find Angle Measures in 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. Section 8.1: Find Angle Measures in Polygons

  2. Polygon • DEFINITION: closed plane figure formed by 3 or more line segments such that each segment intersects exactly 2 other segments only at endpoints These figures arenot polygons These figures are polygons

  3. Vertex • DEFINITION: each endpoint of a side of a polygon • Plural is vertices

  4. Classification of Polygons • Convex: A polygon such that no line containing a side of the polygon contains a point in the interior of the polygon • Non-Convex (concave)- a polygon that is not convex

  5. Equilateral- polygon with all of its sides congruent • Equiangular- polygon with all of its interior angles congruent • Just like we learned with triangles… but now applies to all polygons!

  6. Regular- polygon that has all sides and angles congruent • Irregular- two sides or interior angles are not congruent

  7. Diagonal-segment that joins two nonconsecutive vertices of a polygon

  8. 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

  9. How to find Exterior Angle • The sum of all the exterior angles in a figure is 360. So to find the measure of EACH exterior angle, you divide 360 by the number of sides. • On your chart for n-gon please write under the measure of exterior angle of regular polygon. • Then fill in the rest of the columns.

  10. How to find Interior Angle • Each exterior and interior angle form supplementary angles. • So take 180 – exterior angle to get each interior angle.

  11. Complete page 2 of your notes by yourself. Then check your answers with the person sitting next to you.

  12. We can divide a polygon into triangles by drawing the diagonals from 1 vertex. Ex. Draw the diagonals from vertex A of pentagon ABCDE. You should have formed 3 triangles. Draw the diagonals from vertex T in the hexagon PQRSTU. You should have formed 4 triangles. Compare the # of sides in the polygon with the # of s formed. There are 2 fewer s than sides!!

  13. Learn This Theorem • Therefore, the sum of all of the (interior) angles of a n-gon is (n - 2)180 • So fill in these blanks…. • The sum of the angles of a pentagon is _______  180 = __________ • The sum of the angles of a hexagon is ________  180 = __________

  14. Continue working through your note sheet. • If you have questions raise your hand.

More Related