Section 5.4: Four Sided Polygons By Joe Lenahan

Polygons- closed plane figure made up of several line segments that are joined together. The sides do not cross each other. Exactly two sides meet at every vertex. These are examples of polygons Polygons

JOEL is not a polygon because a polygon consists entirely of segments J O E L P R I C Y PRICY is not a polygon. In a polygon, consecutive sides intersect only at endpoints. Nonconsecutive sides do not intersect

Naming Polygons You name polygons by starting at any vertex and then proceeding either clockwise or counter clockwise A B C D If you start at A, the polygon would be called either ABCD or ADCB

Convex Polygon Convex polygon- Every interior angle is less than 180 o These are all convex polygons

Convex Polygons L M O N P LMNOP is not convex because P is greater then 180 . LMNOP is a concave figure which is a figure in which at least one interior angle is more than 180

Diagonals of Polygons Diagonal- any segment that connects two nonconsecutive vertices of a polygon A B C DE F G H In polygon ABCDEFGH, CH and AF are diagonals

Quadrilaterals Quadrilateral Quadrilateral - four sided polygon Special Quadrilaterals Parallelogram - quadrilateral in which both pairs of opposite sides are parallel and congruent Rectangle - a parallelogram in which at least one angle is right Rhombus -a parallelogram in which at least two consecutive sides are congruent Square - a parallelogram that is both a rhombus and a square

More Special Quadrilaterals Kite- a quadrilateral in which two disjoint pairs of consecutive sides are congruent Trapezoid - a quadrilateral only have one pair of parallel sides, the bases Isosceles Trapezoid - a trapezoid in which the non-parallel sides are congruent

Sample Problems Is this a polygon? The answer is no because a circle doesn’t have any sides or vertices F L N X Starting at point F, what would the name of this polygon be? FLXN or FNXL

More Sample Problems Give the most descriptive names for the following shapes:  congruent The most descriptive name is rectangle The most descriptive name is parallelogram

x3x3 3x  y x4x4 2x-1 1) Find x and y if ABCD is a rectangle. A B C D Practice Problems

Practice Problems Continued Always, Sometimes, Never –A trapezoid is a parallelogram –A square is a rhombus –A polygon is a parallelogram –An isosceles trapezoid is a polygon –A square is an isosceles trapezoid –A parallelogram is a rectangle 2)

Practice Problems Cont’ Name this polygon, stating at point Z and two diagonals Z I O P X F W Y 3)

Answers 1) y=7, x=5 2) N,A,S,A,N,S 3) ZYWFXPOI or ZIOPXFXY, and YP and IX

For Your Enjoyment Just A Boring Square

Bibliography "Polygon Properties." Math.Com: the World of Math Online Math.Com. 30 May Rhoad, Richard, George Milauskas, and Robert Whipple. Geometry for Enjoyment and Challenge. Evanston, Illinois: McDougal Littell, 1991.