A postulate is a statement the is presume true there is no proof. A organize is a true explain that deserve to be proven. Detailed below are six postulates and also the theorems that can be proven from this postulates.

You are watching: Two intersecting lines lie in two planes.

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

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

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

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

*Postulate 5:*If two points lied in a plane, climate the heat joining lock lies in that plane.

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

*Theorem 1:*If 2 lines intersect, climate they intersect in exactly one point.

*Theorem 2:*If a suggest lies external a line, then precisely one aircraft contains both the line and the point.

*Theorem 3:*If 2 lines intersect, then precisely one plane contains both lines.

**Example 1:** State the postulate or theorem friend would use to justify the explain made around each figure.

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

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Through any type of three non-si points, over there is specifically one plane *(Postulate 4)*.

Through any kind of two points, over there is specifically one line *(Postulate 3)*.

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

If 2 planes intersect, then their intersection is a heat *(Postulate 6)*.

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

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

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

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

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