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Section 1.3: Points, Lines, and Planes

Section 1.3: Points, Lines, and Planes. Goal: Be able to understand basic terms and postulates of geometry. Warm up: Solve the system of equations. y = 2x – 4 4x – y = 10. Graphing. Substitution. Elimination. 4x – ( 2x – 4 ) = 10 2x + 4 = 10 2x = 6

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Section 1.3: Points, Lines, and Planes

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  1. Section 1.3: Points, Lines, and Planes Goal: Be able to understand basic terms and postulates of geometry. Warm up: Solve the system of equations. y = 2x – 4 4x – y = 10 Graphing Substitution Elimination 4x – (2x – 4) = 10 2x + 4 = 10 2x = 6 x = 3 -2x + y = - 4 4x – y = 10 2x = 6 x = 3 y = 2(3) – 4 y = 2 y = 2(3) – 4 y = 2 (3, 2) (3, 2) (3, 2)

  2. point - ______________________ ______________________ Location with no size, represented by a small dot, named by a capital letter A ______________________________ ______________________________ a geometric figure consist of a set of points space - ______________________ a boundless, 3-D set of all points

  3. series of points that extends in line - ________________________ ________________________ two opposite directions without end m Q PQ line PQ P line m QP Points that lie in the same line are _______________. collinear points (PQ are collinear)

  4. In the figure below, name 3 points that are collinear and 3 points that are not collinear (noncollinear). X Z W Y Y, Z, and W are collinear Why are arrowheads on the lines? X, Y, and Z are not collinear X, W, and Z are not collinear

  5. Plot __________________________________ __________________________________ A(0, -4), B (2, 2), and C(3, 5) on a coordinate plane. C B A _____________________________________________ _____________________________________________ What are your observations? Points A, B, and C are collinear.

  6. plane - _______________________ _______________________ _______________________ _______________________ a flat surface that has no thickness; contains many lines and extends infinitely far in the direction of its lines. R B C A Plane R Plane ABC *A, B, C are noncollinear points Points and lines in the same plane are ___________. coplanar

  7. 1. Name two different planes that contain points C and G. C G B F D H A E J plane BCG, plane DCG 2. Name the intersection of plane AED and plane HEG. HE 3. How many planes contain the points A, F, and H? 1 (3 noncollinear points)

  8. postulate - _____________________ _____________________ or axiom; an accepted statement of fact Postulate 1-1_________________________ ______________________________ Through any two points,there is exactly one line. m B A

  9. Postulate 1-2 ________________________ ______________________________ If two lines intersect, then they intersect in exactly one point. Postulate 1-3 ________________________ ______________________________ If two planes intersect, then they intersect in exactly one line. P Plane PQR and Plane QRS intersect at QR S Q R

  10. Postulate 1-4 ___________________________ ______________________________ Through any 3 noncollinearpoints there is exactly one plane. B A C Plane ABC

  11. What is the difference between a postulate and a conjecture?

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