6.1 Polygons Day 1

What is polygon?  Formed by three or more segments (sides).  Each side intersects exactly two other sides, one at each endpoint.  Has vertex/vertices.

 Polygons are named by the number of sides they have. Fill in the blank. Number of sidesType of polygon 3Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon

Concave vs. Convex  Convex: if no line that contains a side of the polygon contains a point in the interior of the polygon.  Concave: if a polygon is not convex. interior

Example  Identify the polygon and state whether it is convex or concave. Concave polygon Convex polygon

AA polygon is equilateral if all of its sides are congruent. AA polygon is equiangular if all of its interior angles are congruent. AA polygon is regular if it is equilateral and equiangular.

Decide whether the polygon is regular. ) ) ) ) ) )) ) )

 A Diagonal of a polygon is a segment that joins two nonconsecutive vertices. diagonals

Interior Angles of a Quadrilateral Theorem  The sum of the measures of the interior angles of a quadrilateral is 360°. A B C D m<A + m<B + m<C + m<D = 360°

Example  Find m<Q and m<R. R x P S 2x° Q 80° 70° x + 2x + 70° + 80° = 360° 3x ° = 360 ° 3x = 210 ° x = 70 ° m< Q = x m< Q = 70 ° m<R = 2x m<R = 2(70°) m<R = 140 °

Find m<A A B C D 65° 55° 123°

 Use the information in the diagram to solve for j. 60° 150° 3j ° 60° + 150° + 3j ° + 90° = 360° 210° + 3j ° + 90° = 360° 300 ° + 3j ° = 360 ° 3j ° = 60 ° j = 20