GEOMETRY
GEOMETRY Geometry is a branch of mathematics that deals
with the study of shapes, sizes, figures, spaces, and
all quantities related to the things you see on Earth.
The word geometry is a conglomeration of the
Greek words "geo" and "metron".
Geo: means "Earth"
Metron: means "measurement"
Undefined
Terms in
GEOMETRY
Undefined Terms
❖Points, lines, and planes are
collectively called UNDEFINED
TERMS.
❖This is because of the obvious idea
that it is not possible to define them
formally.
▪ Has NO part.
▪ Has position but with NO spatial
magnitude, size, or dimension.
POINT ▪ Has NO width.
▪ Has NO thickness.
▪ Can be represented by a small dot on
paper using the tip of the pencil.
▪ Locations of places on a map are also
an example of points.
❖Is a geometric figure that
has NO width.
LINE ❖Has NO thickness.
❖Extends indefinitely in
opposite directions.
❖Can be imagined to be a
very long pencil or rope
where the starting point
and the ending point
cannot be seen.
❑Is a surface that lies evenly with straight
lines on itself.
❑Is a two-dimensional (2-D) figure that
HAS length and width.
❑Has NO thickness.
❑Some physical models of a plane include
PLANE wall, floor, and window.
Line Segment:
A line segment is a part of a line
that has two distinct endpoints. It's a
finite portion of a line.
Subsets of a
Line
Ray:
Ray can be defined as a part of a
line that has a fixed starting point but no
endpoint.
Subsets of a
Line
Intersecting,
Perpendicular, and
Parallel Lines
Whenever two lines cross one
another and meet up at a point,
they’re called intersecting lines. The
point where they meet up is called
Intersecting the point of intersection.
Lines
Perpendicular Lines–
Whenever 2 lines intersect precisely
at 90°, they’re called perpendicular
lines.
Perpendicular
Lines
Parallel Lines –2 lines are parallel if
they don’t intersect at any point.
Parallel Lines
Exploring Two-
Dimensional
Figures
Two-dimensional
Circle- the set of all points in a plane that are
Figures equidistant from a given point called the center.
Triangle- a closed figure formed by three
straight line segments called sides, intersecting
at three distinct points called vertices.
Quadrilateral - a closed figure formed by four
straight line segments called sides, which
intersect at four distinct points called vertices.
Exploring
Three-
Dimensional
Figures
Three-
dimensional Rectangular box is also known as rectangular
Figures- prism. A rectangular box is a solid shape with six
rectangular faces, where opposite faces are congruent
and parallel.
POLYHEDRONS
Square Box or Cube is a three-dimensional solid
shape with six square faces, where all faces are
congruent and parallel.
VERTEX face EDGE Pyramid-It is a solid shape with one base.
Commonly, it has 5 vertices, 5 faces, and 8 edges.
Three-
dimensional
Cylinder - is a three-dimensional geometric shape with
Figures with a smooth, curved surface.
Curves
Cone- is a three-dimensional geometric shape with a
pointed tip and a circular base.
Sphere- is a three-dimensional geometric shape that's
perfectly round and symmetrical.
