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

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*Postulate 1:*A line consists of at the very least two points.

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

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

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

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

*Postulate 6:*If 2 planes intersect, then their intersection is a line.

*Theorem 1:*If two lines intersect, climate they crossing in specifically one point.

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

*Theorem 3:*If two lines intersect, then precisely one aircraft contains both lines.

**Example 1:** State the postulate or theorem friend would usage to justify the declare made about each figure.

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

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

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

If 2 points lie in a plane, climate the heat joining castle lies in that airplane *(Postulate 5)*.

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

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

(f)If 2 lines intersect, then specifically one airplane contains both lines *(Theorem 3)*.

If a allude lies outside a line, then specifically one airplane contains both the line and also the allude *(Theorem 2)*.

If 2 lines intersect, climate they intersect in precisely one allude *(Theorem 1)*.

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