![]() If two lines intersect, then they intersect in exactly one point (Theorem 1). Postulate 2: A plane contains at least three noncollinear points. If a point lies outside a line, then exactly one plane contains both the line and the point (Theorem 2). Postulates and Theorems Postulate 1: A line contains at least two points. If two lines intersect, then exactly one plane contains both lines (Theorem 3). If two planes intersect, then their intersection is a line (Postulate 6).Ī line contains at least two points (Postulate 1). If two points lie in a plane, then the line joining them lies in that plane (Postulate 5). Through any two points, there is exactly one line (Postulate 3). Through any three noncollinear points, there is exactly one plane (Postulate 4). Theorem 3: If two lines intersect, then exactly one plane contains both lines.Įxample 1: State the postulate or theorem you would use to justify the statement made about each figure.įigure 1 Illustrations of Postulates 1–6 and Theorems 1–3.Theorem 2: If a point lies outside a line, then exactly one plane contains both the line and the point. ![]()
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