A postulate is a statement that is assumed true without proof. A theorem is a true statement that can be proven. Listed below are six postulates and the theorems that can be proven from these postulates.

*Postulate 1:* A line contains at least two points.

*Postulate 2:* A plane contains at least three noncollinear points.

*Postulate 3:* Through any two points, there is exactly one line.

*Postulate 4:* Through any three noncollinear points, there is exactly one plane.

*Postulate 5:* If two points lie in a plane, then the line joining them lies in that plane.

*Postulate 6:* If two planes intersect, then their intersection is a line.

*Theorem 1:* If two lines intersect, then they intersect in exactly one point.

*Theorem 2:* If a point lies outside a line, then exactly one plane contains both the line and the point.

*Theorem 3:* If two lines intersect, then exactly one plane contains both lines.

**Example 1:** State the postulate or theorem you would use to justify the statement made about each figure.

**Figure 1 **Illustrations of Postulates 1–6 and Theorems 1–3.

Through any three noncollinear points, there is exactly one plane *(Postulate 4)*.

Through any two points, there is exactly one line *(Postulate 3)*.

If two points lie in a plane, then the line joining them lies in that plane *(Postulate 5)*.

If two planes intersect, then their intersection is a line *(Postulate 6)*.

A line contains at least two points (Postulate 1).

If two lines intersect, then exactly one plane contains both lines *(Theorem 3)*.

If a point lies outside a line, then exactly one plane contains both the line and the point *(Theorem 2)*.

If two lines intersect, then they intersect in exactly one point *(Theorem 1)*.