# Math 310 - PowerPoint PPT Presentation

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## Math 310

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Title: Math 310

1
Math 310
• 9.2
• Polygons

2
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 cant be
split into two disjoint sets.

3
Simple Curve
• Def
• A simple curve is a curve that does not cross
itself, with the possible exception of having the
same beginning and ending points.

4
Closed Curve
• Def
• A closed curve is a curve that has the same
beginning and ending point.

5
Polygon
• Def
• 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.

6
Convex and Concave Polygons
• Def
• 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.

7
Polygonal Region
• Def
• 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.

8
Types of Polygons
• Polygons are classified, primarily, according to
the number of sides that they have. This is
summarized in the following table.

9
Types of Polygons (cont)
Polygon Number of Sides (or vertices)
Triangle 3
Pentagon 5
Hexagon 6
Heptagon 7
Octagon 8
Nonagon 9
Decagon 10
n-gon n
10
Parts of a Polygon
• Side
• Vertex
• Interior angle
• Exterior angle
• diagonal

11
Interior Angle
• Def
• An interior angle of a polygon is created by
three consecutive vertices.

12
Exterior Angle
• Def
• An exterior angle of a polygon is created by
extending a side out from the polygon and reading
the angle between the contiguous side.

13
Diagonal
• Def
• A diagonal of a polygon is a segment connecting
any two non-consecutive vertices.

14
Ex
exterior angle
exterior angle
15
Congruency
• Idea
• 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.
• Notation

16
Ex.
17
Regular Polygon
• Def
• A polygon is called regular if all its angles and
sides are congruent.

18
Ex
19
Further Classification of Polygons
• Triangles

20
Triangles
• Right triangle
• Acute triangle
• Obtuse triangle
• Scalene triangle
• Isosceles triangle
• Equilateral triangle

21
Right Triangle
• Def
• A right triangle contains exactly one right angle.

22
Acute Obtuse Triangle
• Def
• An acute triangle contains all acute angles while
an obtuse triangle contains exactly one obtuse
angle.

23
Scalene Triangle
• Def
• A scalene triangle has three non-congruent sides.
(ie all the sides are of different length.)

24
Isosceles Triangle
• Def
• An isosceles triangle has at least two congruent
sides.

25
Equilateral Triangle
• Def
• An equilateral triangle is a triangle with all
sides congruent.

26
• Trapezoid
• Kite
• Isosceles trapezoid
• Parallelogram
• Rectangle
• Rhombus
• Square

27
Trapezoid
• Def
• A 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
Kite
• Def
• A quadrilateral with two non-overlapping pairs of

NON-VERTEX ANGLES
VERTEX ANGLES
30
Parallelogram
• Def
• A parallelogram is a quadrilateral with opposite
sides parallel.

31
Rectangle
• Def
• A rectangle is a parallelogram with a right
angle.

32
Rhombus
• A rhombus is a quadrilateral with four congruent
sides.

33
Square
• A square is a rhombus with a right angle.

34
• 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.

35