Math 310 9.2 Polygons Curve & Connected Idea The 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. Simple Curve Def
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
The 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.
A simple curve is a curve that does not cross itself, with the possible exception of having the same beginning and ending points.
A closed curve is a curve that has the same beginning and ending point.
A 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.
A 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.
A 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.
Polygons are classified, primarily, according to the number of sides that they have. This is summarized in the following table.
An interior angle of a polygon is created by three consecutive vertices.
An exterior angle of a polygon is created by extending a side out from the polygon and reading the angle between the contiguous side.
A diagonal of a polygon is a segment connecting any two non-consecutive vertices.
Two 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.
A polygon is called regular if all its angles and sides are congruent.
A right triangle contains exactly one right angle.
An acute triangle contains all acute angles while an obtuse triangle contains exactly one obtuse angle.
A scalene triangle has three non-congruent sides. (ie all the sides are of different length.)
An isosceles triangle has at least two congruent sides.
An equilateral triangle is a triangle with all sides congruent.
A trapezoid is a quadrilateral with at least one pair of parallel sides.
An isosceles trapezoid is a trapezoid with the non-parallel sides being congruent
A quadrilateral with two non-overlapping pairs of congruent adjacent sides.
A parallelogram is a quadrilateral with opposite sides parallel.
A rectangle is a parallelogram with a right angle.
A rhombus is a quadrilateral with four congruent sides.
A square is a rhombus with a right angle.
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.