After studying this section, you will be able to: 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 c b a d e

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

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

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

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

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

Special Quadrilaterals Sketch What is a … Trapezoid A quadrilateral with exactly 1 pair of parallel sides (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.

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

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

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