Basic Concepts of Geometry

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