All subjects basic Ideas Parallel currently triangle polygon Perimeter and also Area Similarity right Angles one Geometric Solids name: coordinates Geometry

A postulate is a statement the is suspect true there is no proof. A theorem is a true statement that deserve to be proven. Detailed below are 6 postulates and the theorems that have the right to be proven from these postulates.

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Postulate 1: A line contains at least two points. Postulate 2: A airplane contains at least three noncollinear points. Postulate 3: Through any type of two points, there is specifically one line. Postulate 4: Through any kind of three non-si points, there is specifically one plane. Postulate 5: If 2 points lie in a plane, climate the heat joining lock lies in the plane. Postulate 6: If 2 planes intersect, then your intersection is a line. Theorem 1: If 2 lines intersect, then they crossing in exactly one point. Theorem 2: If a suggest lies external a line, then precisely one airplane contains both the line and the point. Theorem 3: If two lines intersect, then specifically one airplane contains both lines.

Example 1: State the postulate or theorem girlfriend would usage to justify the explain made about each figure.

Figure 1Illustrations the Postulates 1–6 and Theorems 1–3.

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(a)

Through any three noncollinear points, there is precisely one airplane (Postulate 4).

(b)

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

(c)

If two points lied in a plane, climate the heat joining them lies in that airplane (Postulate 5).

(d)

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

(e)

A line has at least two point out (Postulate 1).

(f)

If 2 lines intersect, then specifically one aircraft contains both lines (Theorem 3).

(g)

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

(h)

If 2 lines intersect, then they intersect in exactly one point (Theorem 1).

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