M103- PLANE & SOLID GEOMETRY
ACTIVITY TITLE: POLYGONS
LEARNING TARGETS: At the end of the lesson the learner will be able to:
1. Distinguish between convex and concave polygons.
2. Classify polygons according to side.
3. Compute the interior angle sum of convex polygon and the degree measure of each
regular polygon.
4. Recognize special quadrilaterals and special parallelograms.
5. Apply various tests to determine whether a specific quadrilateral is a parallelogram.
6. Enumerate the properties of each quadrilaterals and parallelograms.
7. Apply the Midpoint Theorem for Triangles.
CLASSIFYING POLYGONS
Polygons
Polygon is basically any closed shape which is formed with three or more straight lines. There is no limit in how
many sides will be there in a polygon, it can possess infinite sides, they can have 10 sides or more sides.
Regular Polygon Irregular Polygon
Convex Polygon Concave Polygon
A polygon with an irregular shape. It
In a In a convex
regular polygon,
polygon, all thethe measure
sides of the of the interior
meansInthe
a concave polygon,
sides and at the
angles of leastpolygon
one angle
angleare
polygon is equal,
less than
and180 degrees.
all the It angles
interior is exactly measures
are not equal. more than 180 degrees. The
opposite
are the same.to the concave polygon. The vertices of vertices of a concave polygon are inwards
a convex polygon are always outwards. as well as outwards.
Examples: Example:
A square has all its sides equal to A quadrilateral with unequal sides.
5cm, and all the angles are at 90°. An isosceles triangle has only two
An equilateral triangle has all three
of its sides equal, and the third side
sides equal to 10cm and angles has a different measurement.
measure to 60°.
Example: Seepentagon
A regular the figurehas
of5anequal
irregular hexagon,
whose vertices are outwards.
sides and all the interior angles
measures to 108 degrees.
, M103- PLANE & SOLID GEOMETRY
Trigons
Trigons are polygons who have three sides. They are nothing but triangles. These trigons or triangles are further
classified into different categories, such as:
Scalene Triangle: All sides are unequal
Isosceles Triangle: Two sides are equal
Equilateral Triangle: All the three sides are equal and all angles measures to 60 degrees.
Equilateral Polygons
HexagonsPolygon
Quadrilateral Pentagon Polygon
The polygons whose all the sides are equal
Another type of
Quadrilateral polygon
polygon is is thecalled
also hexagon which
a four- Theare
five-sided polygon ispolygons,
called pentagon polygon.
called equilateral for example,
has 6 sides
sided and or
polygon 6 vertices. A regular
a quadrangle. The hexagon
different Whenan all the five sides
equilateral of the
triangle, polygon
a square, etc.are equal in
will
types of the quadrilateral polygoninterior
have equal 6 sides and all its and
are square, length, then it is called regular pentagon otherwise
exterior angles
rectangle, also measure
rhombus equals.
and parallelogram. irregular pentagon.
Equiangular Polygons
The polygons whose all the interior angles
are equal such as a rectangle are called
equiangular polygons.
ANGLE SUM OF POLYGONS
Sum of angles of a polygon = (n-2) x 180°
Let’s look at some example
SHAPES NO. OF SIDES SUM OF THE ANGLES
3 (3-2) = 1x180° = 180°
ACTIVITY TITLE: POLYGONS
LEARNING TARGETS: At the end of the lesson the learner will be able to:
1. Distinguish between convex and concave polygons.
2. Classify polygons according to side.
3. Compute the interior angle sum of convex polygon and the degree measure of each
regular polygon.
4. Recognize special quadrilaterals and special parallelograms.
5. Apply various tests to determine whether a specific quadrilateral is a parallelogram.
6. Enumerate the properties of each quadrilaterals and parallelograms.
7. Apply the Midpoint Theorem for Triangles.
CLASSIFYING POLYGONS
Polygons
Polygon is basically any closed shape which is formed with three or more straight lines. There is no limit in how
many sides will be there in a polygon, it can possess infinite sides, they can have 10 sides or more sides.
Regular Polygon Irregular Polygon
Convex Polygon Concave Polygon
A polygon with an irregular shape. It
In a In a convex
regular polygon,
polygon, all thethe measure
sides of the of the interior
meansInthe
a concave polygon,
sides and at the
angles of leastpolygon
one angle
angleare
polygon is equal,
less than
and180 degrees.
all the It angles
interior is exactly measures
are not equal. more than 180 degrees. The
opposite
are the same.to the concave polygon. The vertices of vertices of a concave polygon are inwards
a convex polygon are always outwards. as well as outwards.
Examples: Example:
A square has all its sides equal to A quadrilateral with unequal sides.
5cm, and all the angles are at 90°. An isosceles triangle has only two
An equilateral triangle has all three
of its sides equal, and the third side
sides equal to 10cm and angles has a different measurement.
measure to 60°.
Example: Seepentagon
A regular the figurehas
of5anequal
irregular hexagon,
whose vertices are outwards.
sides and all the interior angles
measures to 108 degrees.
, M103- PLANE & SOLID GEOMETRY
Trigons
Trigons are polygons who have three sides. They are nothing but triangles. These trigons or triangles are further
classified into different categories, such as:
Scalene Triangle: All sides are unequal
Isosceles Triangle: Two sides are equal
Equilateral Triangle: All the three sides are equal and all angles measures to 60 degrees.
Equilateral Polygons
HexagonsPolygon
Quadrilateral Pentagon Polygon
The polygons whose all the sides are equal
Another type of
Quadrilateral polygon
polygon is is thecalled
also hexagon which
a four- Theare
five-sided polygon ispolygons,
called pentagon polygon.
called equilateral for example,
has 6 sides
sided and or
polygon 6 vertices. A regular
a quadrangle. The hexagon
different Whenan all the five sides
equilateral of the
triangle, polygon
a square, etc.are equal in
will
types of the quadrilateral polygoninterior
have equal 6 sides and all its and
are square, length, then it is called regular pentagon otherwise
exterior angles
rectangle, also measure
rhombus equals.
and parallelogram. irregular pentagon.
Equiangular Polygons
The polygons whose all the interior angles
are equal such as a rectangle are called
equiangular polygons.
ANGLE SUM OF POLYGONS
Sum of angles of a polygon = (n-2) x 180°
Let’s look at some example
SHAPES NO. OF SIDES SUM OF THE ANGLES
3 (3-2) = 1x180° = 180°
