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5.4 Four Sided Polygons

5.4 Four Sided Polygons. Objective: After studying this section, you will be able to: Recognize polygons, Understand how polygons are named, Recognize convex polygons, Recognize diagonals of polygons, and Identify special types of quadrilaterals. Polygons are plane figures. Non-polygons.

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5.4 Four Sided Polygons

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  1. 5.4 Four Sided Polygons Objective: After studying this section, you will be able to: Recognize polygons, Understand how polygons are named, Recognize convex polygons, Recognize diagonals of polygons, and Identify special types of quadrilaterals.

  2. Polygons are plane figures.

  3. Non-polygons c b a d e

  4. So, polygons must have: Segments Consecutive sides intersect only at endpoints Nonconsecutive sides should not intersect Each vertex must belong to only two sides Segments must meet at a vertex Consecutive sides must be noncollinear

  5. To name a polygon begin at any vertex and proceed either clockwise or counterclockwise around the figure. A B C F E D

  6. Definition: A convex polygon is a polygon in which each interior angle has a measure less than 180. Convex Not convex (concave)

  7. Definition: A diagonal of a polygon is any segment that connects two nonconsecutive (nonadjacent) vertices of the polygon.

  8. What is a quadrilateral? It is a four-sided polygon.

  9. Special Quadrilaterals Trapezoid A quadrilateral with exactly 1 pair of parallelsides (bases). Isosceles A trapezoid in which the non- Trapezoid parallel sides (legs) are congruent. (lower and upper base angles) Kite A quad with 2 disjoint pairs of consecutive congruent sides. Sketch What is a …

  10. Parallelogram A quad with 2 sets of parallel sides. Rhombus A parallelogram in which at least two consecutive sides are congruent. What is a Sketch

  11. Rectangle A parallelogram with at least one right angle. Square A parallelogram that is both a rectangle and a rhombus. Sketch What is a

  12. Quadrilateral Parallelogram Trapezoid Square Rhombus Rectangle Isosceles Trapezoid Kite • Trapezoid b. Rectangle C. Square D. Quadrilateral • e. Rhombus f. Isosceles Trapezoid g. Parallelogram h. Kite

  13. Summary Describe the difference between convex and concave. Explain how you will remember the special quadrilaterals. Homework: worksheet

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