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

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(a)

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

(b)

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

(c)

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

(d)

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

(e)

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).

(g)

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

(h)

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

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