Postulates Common Notions

Postulate 1. To draw a straight line fromany point to any point.

Common notion 1. Things which equal the samething also equal one another.

Postulate 2 To produce a finite straightline 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 anycenter and radius.

Common notion 3. If equals are subtracted fromequals, then the remainders are equal.

Postulate 4. That all right angles equal oneanother.

Common notion 4. Things which coincide withone another equal one another.

Postulate 5. Given a line and a point not onthe line there exists exactly oneline through the point andparallel to the given line.

Common notion 5. The whole is greater than thepart.

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.

A

B

C

A

B

C

Alternate interior angles are equal.

Vertical Angles are equal.

Alternate exterior angles are equal.

Corresponding angles are equal.

A

B

C

C A

A

B

C

A

B

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.