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6.1 Polygons

Explore the world of polygons, from triangles to octagons, understanding their sides, vertices, and interior angles. Learn the difference between convex and concave polygons, as well as what makes a polygon regular. Find out how to calculate interior angles and identify diagonal lines. Dive into the fascinating realm of polygons!

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6.1 Polygons

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  1. 6.1 Polygons Day 1

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

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

  4. 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

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

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

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

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

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

  10. Example • Find m<Q and m<R. x + 2x + 70° + 80° = 360° 3x + 150 ° = 360 ° 3x = 210 ° x = 70 ° Q x 2x° R 80° P 70° m< Q = x m< Q = 70 ° m<R = 2x m<R = 2(70°) m<R = 140 ° S

  11. Find m<A C 65° D 55° 123° B A

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

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