1. The intersection of two lines is a point.

2. The intersection of two planes is a line.

3. Through any two points there is exactly one line.

4. Through any three noncollinear points there is exactly one plane.

5. If two points are in a plane, the the line containing them is in that plane.

6. *Segment Congruence Postulate:*

a. If two segments have the same length as measured by a fair ruler (a ruler that has evenly spaced segments marked), **then the segments are congruent. **

b. If two segments are congruent, **then they have the same length as measured by a fair ruler.**

7. *Segment Addition Postulate:*

If a line contains three points (let us call the points A, B, and C) and point B is between points A and C, **then AB + BC = AC**. AB is the length of segment AB, and BC is the length of segment BC and AC is the length of segment AC.

8. *Angle Congruence Postulate:*

If two angles have the same measure (the rays do not have to have the same length), **then they are congruent.** If two angles are congruent, **then they have the same measure.**

9. *Angle Addition Postulate:*

Suppose we have three noncollinear points, A, B, and C, and through each of these points there is a ray. Then suppose these three rays meet at a fourth point, D. If point B is in the interior of angle ADC, **then the measure of angle ADB + the measure of angle BDC = the measure of angle ADC. **

Polygon Congruence Postulate: Two polygons are congruent** if and only if **there is a correspondence between their sides and angles such that:

Each pair of corresponding angles is congruent.

Each pair of corresponding sides is congruent.

SSS (Side-Side-Side) Postulate

SAS (Side-Angle-Side) Postulate

ASA (Angle-Side-Angle) Postulate

Midpoint formula: The midpoint of a segment with endpoints and has the following coordinates: