A postulate is a statement that is assumed true without proof. A theorem is a true statement that deserve to be prcooktop. Listed listed below are 6 postulates and also the theorems that can be prrange from these postulates.

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*Postulate 1:*A line has at least 2 points.

*Postulate 2:*A aircraft has at least 3 noncoldirect points.

*Postulate 3:*Thturbulent any type of 2 points, tbelow is specifically one line.

*Postulate 4:*Thunstable any type of three noncoldirect points, there is exactly one airplane.

*Postulate 5:*If 2 points lie in a plane, then the line joining them lies in that airplane.

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

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

*Theorem 2:*If a point lies external a line, then specifically one aircraft consists of both the line and also the suggest.

*Theorem 3:*If two lines intersect, then exactly one airplane has both lines.

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

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

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Thturbulent any three noncolstraight points, there is specifically one airplane *(Postulate 4)*.

Thunstable any kind of 2 points, there is precisely one line *(Postulate 3)*.

If 2 points lie in a aircraft, then the line joining them lies in that plane *(Postulate 5)*.

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

A line consists of at least 2 points (Postulate 1).

(f)If two lines intersect, then precisely one plane consists of both lines *(Theorem 3)*.

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

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

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