Polygons

Discussion

• A polygon is a closed figure in a plane determined by three or more line segments.
  • Sides
  • Verities, or vertex
  • regular - if all the sides are the same length.
• a triangle is the simplest, but perhaps the most useful.
• Look at table 9.1, pg 485 for shape names.
• Show how to prove that the sum of the interior angles of a triangle are 180°
  • Review vertical angles
  • Review alternate interior angles
  • 
• Can we figure out the size of the angles of a regular n-gon?
  • In an n-gon, we know that all of the angles are equal
  • We can carve the n-gon into triangles
  • We can find the total sum of all of the angles within the n-gon
  • We can divide this by the number of angles.
  • S = (n-2)*180
  • M = (n-2)*180/n
• Triangles, see page 487 for definitions
  • Right triangle - one angle is 90°
  • Equilateral triangle - all sides and angles are equal.
  • Isosceles triangle - two sides (and angles) are equal.
  • Scalene triangle, no two sides are equal.
  • Obtuse triangle - one angle is > 90°
  • Acute triangle - all angles < 90°
• Similar Figures
  • Two polygons are similar if their corresponding angles are the same.
• Two figures are congruent if they have identical corresponding sides and angles.

Examples

• 30
• 32
• 34
• 48
• 50

Homework