1. 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.

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
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
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
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.

10. 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.

11. 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.

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