Basic Geometry - Lines
Basic Geometry figures
Basic geometry figures are point, lines, line segment, ray of line, and plane.
Point
Point has position but has no shape or size.
Line
Line is the path described by a moving point, has an infinite number of points, has no width, can be determined by two points, can be straight or curved, and extend indefinitely.
Segment of line
A part of a line between two end points, has length, and formed when we use a ruler to join two point.
Ray of line
A part of a line with one end point, extend indefinitely on one direction only.
Plane
A Flat surface in which any two points are joined by a straight line lying entirely on the surface, has no thickness, Extend infinitely in all direction.
Position of lines.
Position of two lines is divided into four as follow:
Parallel
Two lines are called parallel if both of lines do not have point of intersection in the same plane.
Two lines are called parallel if both of lines do not have point of intersection in the same plane.
Intersect
Two lines are called intersect if both lines have exactly one point of intersection.
Cross section
Two lines are called in a cross section if both lines do not intersect each other and laid in a different plane.
Coincide
Two lines are called coincide if both lines have at least two points of intersection.
Coincide
Two lines are called coincide if both lines have at least two points of intersection.
Note:
- Through one point can be drawn lines in unlimited number.
- If there is two points then a line can be drawn from it.
- The distance from a point to a line is equal to the length of a line which is drawn from the point and perpendicular to the line.
Segment of line Addition
In a line can be drawn unlimited point. if a point is added between two another points as in the following figure then it is applied the addition and subtraction of line segment.
The addition postulate:
AB = AC + CB
The subtraction Postulate:
AC = AB - CB and BC = AB - AC
Example 1:
Point A and B are laid in a straight line. These points are separated 14 cm each other. If point C is drawn between point A and B and Segment line AB is divided into ratio 4 : 3, determine the distance of point C from point B.
Solution:
Draw the sketch of the problem.
Ratio 4 : 3 can be written as 4x : 3x then from the sketch:
4x + 3x = 14 (addition postulate)
7x = 14
x = 2
since the value of x = 2 then the distance from point B to C is:
3x = 3 . 2 = 6 cm.
-Vn-
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