Polygons b.ing math. citra
english math. II
Published on: Mar 4, 2016
Transcripts - Polygons b.ing math. citra
Citra Triwana Marpaung
ACA 111 0050
Angles in Polygons
The vertex angles of a polygons with four or
more sides can be any size between 0˚ and 360˚.
In the hexagon figure, we
can known that,
B is less than 20˚ and
D and A are both
greather than 180˚.
In spite of this range of possible size, there is a relationship
between the sum of all the angles in polygon and its number sides.
In any triangle, the sum of the three angle
measures is 180˚. One way of demostrating that
theorem is to draw an abitrary triangle and cut off
The sum of the angles in a polygon with four or more sides can
be found by subdividing the polygon into triangels so that the
vertices of the triangles are the vertice of the polygon.
In quadrilateral in that figure above is partitioned into two triangles.
Thus, the sum of all angles (six angel of both the triangles) is
2 triangles x 180˚ = 360˚
However, since each the quadrilateral can be partitioned into
triangles such that the vertices of triangles are also the vertices of
a quadrilateral, the sum of the angles a quadrilateral will always
Similar approach can be used to find the sum of the angles in any
The total number
of degrees in its
3 x 180˚ = 540˚
The idea of Congruence is one figure can be placed on the
other, so that they coincide.
Another way to describe congruent plane figures is to say
that they have same size and shape.
Two line segments are congruent if they have the same
length. And two angles are congruent if they have same
The figures in those photographs are examples of regular polygons.
A polygon is called a regular polygon if it satisfies
both of the folloeing conditions:
1. All angles are congruent.
2. All sides are congruent
Regular pentagon Equilateral triangle square
Drawing Regular Polygons
Three special angles in regular polygons.
A vertex angle
is formed by two adjacent sides of polygon
A central angle
is formed by connecting the centerof
the polygon to two adjacent vertices
is formed by one side of the polygon
and the extension of an adjacent
The sum of the measures of the angles in a polygon can be used
to compute the number of degrees in each vertex angle of a
regular polygon; Simply divide the sum of all the measures of the
angles by the number of angles.
The sum angles in pentagon is
3 triangles x 180˚ = 540˚
Therefore, each angle in a regular
540˚ 5 vertex angles = 108˚
Steps of Drawing a Regular Polygon
Step(1) Draw a line segment
and mark a vertex
Step(2) Measure off a 108˚ angle
Step(3) Mark off two sides of
Step(4) Measure off a second
angle of 108˚
Antother approach to drawing regular polygons begins with a
circle and uses central angles.
The number of degrees in the central angle of a regular polygon
is 360˚ devided by the number of sides in the polygon.
A decagonhas 10 sides, then each
central angle is 360˚ 10 = 36˚
Tessellation With Polygons
Any arrangement in which no overlapping figures are
placed together to entirely cover a region is called a
Floors and ceilings are often tesselated with square-
shaped material, because squares can be joined together
without gaps or overlaps
A regular hexagon
These three types that will tessellate by themselves
Tessellation with regular hexagon
The points at which the
vertices of the hexagon meet
are the vertex points of the
A tessellation of two or more noncongruent regular polygons in which
each vertex is surrounded by the same arrangement of polygons, called
SEMIREGULAR NOT SEMIREGULAR
Problem Solving Application
Consider a regular polygon with fewer sides. A regular
hexagon has six congruent vertex angle, and since it can
be partitioned into four triangles.
What is the number of degrees in one of its vertex angles?
What is the size of each vertex angles in hexagon?
4 x 180˚ = 720˚
720˚ 6 = 120˚