2 Curve & ConnectedIdeaThe idea of a curve is something you could draw on paper without lifting your pencil.The idea of connected is that a set can’t be split into two disjoint sets.
3 Simple CurveDefA simple curve is a curve that does not cross itself, with the possible exception of having the same beginning and ending points.
4 Closed CurveDefA closed curve is a curve that has the same beginning and ending point.
5 PolygonDefA polygon is a planar figure, that is a simple closed curve consisting entirely of straight segments. Where two segments meet is called a vertex of the polygon. Each segment is called a side of the polygon.
6 Convex and Concave Polygons DefA convex polygon is one in which every point in the interior of the polygon can be joined by a line segment that stays entirely inside the polygon. A concave polygon would be one in which there exist at least two points, such that when joined by a line segment, the segment passes outside of the polygon.
7 Polygonal RegionDefA polygon divides the plane its in, into three regions, the interior, exterior, and the curve itself. The interior and the curve itself comprise the polygonal region we are concerned with.
8 Types of PolygonsPolygons are classified, primarily, according to the number of sides that they have. This is summarized in the following table.
9 Types of Polygons (cont) Number of Sides (or vertices)Triangle3Quadrilateral4Pentagon5Hexagon6Heptagon7Octagon8Nonagon9Decagon10n-gonn
10 Parts of a PolygonSideVertexInterior angleExterior anglediagonal
11 Interior AngleDefAn interior angle of a polygon is created by three consecutive vertices.
12 Exterior AngleDefAn exterior angle of a polygon is created by extending a side out from the polygon and reading the angle between the contiguous side.
13 DiagonalDefA diagonal of a polygon is a segment connecting any two non-consecutive vertices.
14 Ex exterior interior interior angle exterior angle side vertex diagonalexterior angle
15 CongruencyIdeaTwo segments are congruent if the tracing of one can be fitted exactly onto the other. Two angles are congruent if their measures are the same. Two polygons are congruent if all their parts are congruent.Notation:
27 TrapezoidDefA trapezoid is a quadrilateral with at least one pair of parallel sides.
28 Isosceles Trapezoid Def An isosceles trapezoid is a trapezoid with the non-parallel sides being congruent
29 KiteDefA quadrilateral with two non-overlapping pairs of congruent adjacent sides.NON-VERTEX ANGLESVERTEX ANGLES
30 ParallelogramDefA parallelogram is a quadrilateral with opposite sides parallel.
31 RectangleDefA rectangle is a parallelogram with a right angle.
32 RhombusA rhombus is a quadrilateral with four congruent sides.
33 SquareA square is a rhombus with a right angle.
34 Quadrilateral Hierarchy By looking at the definitions, we see that some of the quadrilateral definitions fulfill one or more of the other definitions automatically. For example, the definition of a square also satisfies the definition of a rhombus. This allows us to set up a hierarchy among the quadrilaterals which will be very useful when discussing their various properties.