Presentation ~ above theme: "Section 2.4 In Geometry, rules that are accepted without evidence are referred to as postulates or axioms. Rules that are showed are referred to as theorems. Postulates."— Presentation transcript:




You are watching: A rule that is accepted without proof

1 ar 2.4 In Geometry, rules the are embraced without proof are dubbed postulates or axioms. Rules the are confirmed are referred to as theorems. Postulates and theorems are regularly written together conditional statements. Unequal the converse that a definition, the converse the a postulate or theorem cannot be assumed to it is in true.

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2 Postulates

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3 points Postulate 1. A line has at the very least two points. 2. A plane contains at the very least 3 noncollinear points. M t

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4 line Postulate Through any type of two points over there exists specifically one line.

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5 Intersection of lines PostulateIf 2 lines intersect, then their intersection is a point. A b

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6 plane Postulate Through any type of three noncollinear points over there is precisely one plane.

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7 Flat airplane Postulate If two points lie in a plane, climate the heat containing lock lies in the plane. S

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8 Intersection of airplane PostulateIf 2 planes intersection then your intersection is a line.

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9 Algebraic link 1. One means to graph a linear equation is come plot 2 points whose works with satisfy the equation and then connect them v a line. (Line Postulate) 2. One means to discover a typical solution that two linear equations is to graph the lines and find the coordinates of their intersection. (Line Intersection Postulate)

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10 instance 1 State the postulate illustrated by the diagram. Plane Postulate

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11 instance 2 usage the diagram to write examples of component 2 that the points Postulate and the aircraft Intersection Postulate. Component 2 of the clues Postulate: airplane Q includes points V, Y, and also W. Plane Intersection Postulate: The intersection of plane Q and airplane P is heat b.

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12 Interpreting a DiagramWhen you interpret a diagram, you have the right to assume information about size or measure only if it is marked.

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13 1. Have the right to assume every points room coplanar1. Can assume all points room coplanar. Cannot assume points E, F, and G space collinear. 2. Deserve to assume CJD and DJE room a straight pair. Can not assume present CE and also BF intersect. 3. Have the right to assume CJD and HJE are vertical angles. Can not assume present CE and also BF do not intersect.

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14 4. Deserve to assume point out A, H, J, and D are collinear4. Can assume point out A, H, J, and also D space collinear. Can not assume CJD  BHJ. 5. Can assume present CE and ad intersect at suggest J. Can not assume present CE and ad are perpendicular or mCJD = 90°.

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15 example 3

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16 A line is a heat perpendicular come a aircraft if and only if the heat intersects the plane in a suggest and is perpendicular to every line in the airplane that intersects the at that point. K

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17 example 4 i beg your pardon of the adhering to statements can not be assumed indigenous the diagram? 1. E, D, and also C are collinear. 2.

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The intersection of line BD and line EC is D. #3 and also #4

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