All topics an essential Ideas Parallel lines triangle polygons Perimeter and also Area Similarity right Angles one Geometric Solids name: coordinates Geometry

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

You are watching: Two intersecting lines lie in two planes.


Postulate 1: A line has at least two points. Postulate 2: A aircraft contains at least three noncollinear points. Postulate 3: Through any kind of two points, over there is exactly one line. Postulate 4: Through any kind of three noncollinear points, there is exactly one plane. Postulate 5: If two points lied in a plane, climate the heat joining lock lies in that plane. Postulate 6: If two planes intersect, then your intersection is a line. Theorem 1: If 2 lines intersect, climate they intersect in exactly one point. Theorem 2: If a suggest lies external a line, then precisely one aircraft contains both the line and the point. Theorem 3: If 2 lines intersect, then precisely one plane contains both lines.

Example 1: State the postulate or theorem friend would use to justify the explain made around each figure.

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Figure 1Illustrations that 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 plane (Postulate 4).

(b)

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

(c)

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

(d)

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

(e)

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

(f)

If two lines intersect, then exactly one plane contains both lines (Theorem 3).

(g)

If a point lies outside a line, then specifically one plane contains both the line and the suggest (Theorem 2).

(h)

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


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