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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 1Illustrations 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).


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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