Postulates
Commo n Notions
Postulate 1.
To draw a straight line from
any point to
any point.
Common notion 1.
Things which equal the same
thing also equal
one another.
Postulate 2
To produce a finite straight
line
continuously in a straight line.
Common notion 2.
If equals are added to equals,
then the wholes
are equal.
Postulate 3.
To describe a circle with any
center and
radius.
Common notion 3.
If equals are subtracted from
equals, then the
remainders are equal.
Postulate 4.
That all right angles equal one
another.
Common notion 4.
Things which coincide with
one another equal
one another.
Postulate 5.
Given a line and a point not on
the line there exists exactly one
line thr ough the point and
parallel to the given line.
Common notion 5.
The whole is greater than the
part.
The distance from any point on
a circle to the center is a
constant called the radius.
The length of any line segment
from a point on a circle to the
center of the circle is a
constant called the radius.
All radii of a circle are the same
length.
B
A
C
B
A
C
Alternate interior angles are
equal.
Vertical Angles are equal.
Alternate exterior angles are
equal.
Corresponding angles are
equal.
C
A
B
A
C
B
A
C
B
A
C
B
A
Proposition 4. SAS Congruence Theorem
If two triangles have two sides and the
angle included (formed) by the sides
equal, then the triangles are congruent.
Remember: things that are congruent are
equal, in every respect.
Proposition 5.
Base angles of an isosceles
triangle are equal.
Proposition:
Bisect a given angle.
Propostion 8. SSS Congruence Theorem
If two triangles have all three sides equal,
then the triangles are congruent.
Remember: things that are congruent are
equal, in every respect.