If two lines intersect, then they intersect in exactly one point (Theorem 1). If a point lies outside a line, then exactly one plane contains both the line and the point (Theorem 2). 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.Theorem 1: If two lines intersect, then they intersect in exactly one point.Postulate 6: If two planes intersect, then their intersection is a line.Postulate 5: If two points lie in a plane, then the line joining them lies in that plane.Postulate 4: Through any three noncollinear points, there is exactly one plane.Postulate 3: Through any two points, there is exactly one line.Postulate 2: A plane contains at least three noncollinear points.Postulate 1: A line contains at least two points.Listed below are six postulates and the theorems that can be proven from these postulates. A theorem is a true statement that can be proven. Summary of Coordinate Geometry FormulasĪ postulate is a statement that is assumed true without proof.Slopes: Parallel and Perpendicular Lines.Similar Triangles: Perimeters and Areas.Proportional Parts of Similar Triangles.Formulas: Perimeter, Circumference, Area.Proving that Figures Are Parallelograms.Postulate is used to derive the other logical statements to solve a. Triangle Inequalities: Sides and Angles Postulate is a true statement, which does not require to be proved.Special Features of Isosceles Triangles In mathematics, the ruler postulate states that on a number line or a ruler, any two points can be named as numbers, or coordinates, and the distance between the two coordinates is their.Classifying Triangles by Sides or Angles.Lines: Intersecting, Perpendicular, Parallel.
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