Basic Concepts of
Geometry
Points and lines
are two of the most fundamental concepts in Geometry, but they are also the
most difficult to define but the most fundamental geometric form is a point. It
is represented as a dot with a capital alphabet which is its name a line is a
set of points and it extends in opposite directions up to infinity.
Geometry: The branch of mathematics concerned with the properties and relations of
points, lines, surfaces, solids, and higher dimensional analogs
Plane: A plane
has obviously no size and definitely no shape. However it is represented as a
quadrangle and a single capital letter.
Lines: A
line we specify a line with two points
is straight (no curves) extends in both directions
without end (infinitely).
If it does have ends it is called a Line Segment.
Point: A point is an exact location in space, points are
dimensionless.
Line
Segment:A line
segment is a part of a line. It has a fixed length and consequently two end
points. They are used to name the line segment
Rays and
Angles: Extend the line segment beyond only one of the original two points. A
ray extends indefinitely in one direction, but ends at a single point in the
other direction. That point is called the end-point of the ray.
Angles
Angle: An angle is a figure formed by two rays with a
common endpoint which are not on the same line. The common endpoints of the
sides of an angle is called the vertex.
Measure of an angle: Every angle
has a measure. It is measured in degrees from 00to 1800 and is
represented as m . A line is
also an angle because it satisfies the definition of having two rays going in
different in this case opposite )
directions with a common end point
Right angle: Has a measure of 900.
Acute angle: Any angle whose measure is between 0 and 900
Obtuse angle: An angle with a measure between 00 and 1800
Reflex Angle: Is
more than 180° but less than 360°
straight
angle: Is 180 degrees
Polygons
Polygons:
Is a closed plane
figure formed by connecting three or more segments at their endpoints.
Triangles
Triangles
can be classified according to the number of congruent sides and their angles.
Equilateral, isosceles and scalene triangles may be
classified according to their congruent sides, and Acute,
Obtuse and right triangles may be classified according to their angles
Triangle: A triangle is a polygon with three sides.
Quadrilateral
A Quadrilateral: is a polygon with four sides, and four vertices
or corners.
Circles
A circle is the set of all points in a plane that are equidistant from a
fixed point in the plane.
Radius: is also used to name a line segment that joins the center of the
circle to the point on the circle.
Diameter: is a line which passes through the center of a circle. It is twice the
length of the radius.
Secant: is a line that contains a chord.
Tangent: a ray or a segment in the plane of a circle that intersects the circle
at exactly one point