5.4 Four Sided Polygons Objective: After studying this section, you will be able to: a. Recognize polygons, b. Understand how polygons are named, c. Recognize.

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

Polygons are plane figures.

Non-polygons a b c e d

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

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

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 nonconsecutive (nonadjacent) vertices of the polygon.

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

Special Quadrilaterals 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. 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. What is a Sketch

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

a.Trapezoidb. RectangleC. SquareD. Quadrilateral e. Rhombusf. Isosceles Trapezoidg. Parallelogramh. Kite Quadrilateral Trapezoid Isosceles Trapezoid Parallelogram RhombusRectangle Square Kite

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