PART D - POSTULATES
3-6. Basic Concepts of Postulates
. Fundamental principles
of geometry that depend
observation and must be taken without proof are called postulates. Postulates are used to develop rules
for other branches of mathematics and to prove many arithmetic and algebraic relationships. The basic
postulates are that-
a. A straight line is the shortest distance between two points.
b. Only one straight line can be drawn between the same two points.
c. Two straight lines cannot intersect at more than one point.
d. A straight line may be extended indefinitely.
e. A straight line may be drawn from a point to any other point.
f. A geometric figure may be moved from one position to another without any change in form
g. All right angles (90€ angles) are equal.
h. All straight angles (180€ angles) are equal.
i. Only one perpendicular line can be drawn from a point in a line in a plane.
j. Only one perpendicular line can be drawn from a point outside a line in a plane.
k. Two adjacent angles which have their exterior sides in a straight line are called
l. The sum of all angles about a point on one side of a straight line in a plane is equal to two
right angles (180€).
m. The sum of all angles about a point in a plane is equal to four right angles (360€).
n. Angles that have the same supplement are equal, and angles that have the same complement
o. Vertical angles are equal.
p. A line segment can be bisected in only one point.
q. An angle can be bisected by only one line.
r. The sides of a square are equal.