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Grade 6 3.01 Identify intersections in a plane

Grade 6 3.01 Identify intersections in a plane. Point, Line, Plane. B. A. A. Points. Points do not have actual size. How to Sketch: Using dots How to label: Use capital letters Never name two points with the same letter (in the same sketch). A. B. A. C. Lines.

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Grade 6 3.01 Identify intersections in a plane

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  1. Grade 63.01 Identify intersections in a plane Point, Line, Plane B A A Lesson 1-1 Point, Line, Plane

  2. Points • Points do not have actual size. • How to Sketch: Using dots • How to label: Use capital letters Never name two points with the same letter (in the same sketch). A B A C Lesson 1-1 Point, Line, Plane

  3. Lines • Lines extend indefinitely and have no thickness or width. • How to sketch : using arrows at both ends. • How to name: 2 ways (1) small script letter – line n (2) any two points on the line - • Never name a line using three points - n A B C Lesson 1-1 Point, Line, Plane

  4. Collinear Points • Collinear points are points that lie on the same line. (The line does not have to be visible.) • A point lies on the line if the coordinates of the point satisfy the equation of the line. Ex: To find if A (1, 0) is collinear with the points on the line y = -3x + 3. Substitute x = 1 and y = 0 in the equation. 0 = -3 (1) + 3 0 = -3 + 3 0 = 0 The point A satisfies the equation, therefore the point is collinear with the points on the line. A B C Collinear C A B Non collinear Lesson 1-1 Point, Line, Plane

  5. Planes • A plane is a flat surface that extends indefinitely in all directions. • How to sketch: Use a parallelogram (four sided figure) • How to name: 2 ways (1) Capital script letter – Plane M (2) Any 3 non collinear points in the plane - Plane: ABC/ ACB / BAC / BCA / CAB / CBA A M B C Horizontal Plane Vertical Plane Other Lesson 1-1 Point, Line, Plane

  6. Different planes in a figure: A B Plane ABCD Plane EFGH Plane BCGF Plane ADHE Plane ABFE Plane CDHG Etc. D C E F H G Lesson 1-1 Point, Line, Plane

  7. Other planes in the same figure: Any three non collinear points determine a plane! Plane AFGD Plane ACGE Plane ACH Plane AGF Plane BDG Etc. Lesson 1-1 Point, Line, Plane

  8. Coplanar Objects Coplanar objects (points, lines, etc.) are objects that lie on the same plane. The plane does not have to be visible. Are the following points coplanar? A, B, C ? Yes A, B, C, F ? No H, G, F, E ? Yes E, H, C, B ? Yes A, G, F ? Yes C, B, F, H ? No Lesson 1-1 Point, Line, Plane

  9. Intersection of Figures The intersection of two figures is the set of points that are common in both figures. The intersection of two lines is a point. m Line m and line n intersect at point P. P n Continued……. Lesson 1-1 Point, Line, Plane

  10. 3 Possibilities of Intersection of a Line and a Plane (1) Line passes through plane – intersection is a point. (2) Line lies on the plane - intersection is a line. (3) Line is parallel to the plane - no common points. Lesson 1-1 Point, Line, Plane

  11. Intersection of Two Planes is a Line. B P A R Plane P and Plane R intersect at the line Lesson 1-1 Point, Line, Plane

  12. Draw a pictureIntersections in the plane • A line and a triangle are in the same plane. The line intersects the triangle at exactly one point, P. Which statement is true? A) P is a vertex of the triangle. B) P is a midpoint of a side of the triangle. C) P is in the interior of the triangle. D) P is in the exterior of the triangle. Lesson 1-1 Point, Line, Plane

  13. Draw a pictureIntersections in the plane • What is the maximum possible number of points of intersection between an equilateral triangle and a circle in the same plane? • A 3 • B 4 • C 6 • D 7 Lesson 1-1 Point, Line, Plane

  14. Explain • Radius FH is 7 cm. H What is the length of the longest chord of circle H? A) 7 cm C) 14 cm B) 9 cm D) 21 cm F Lesson 1-1 Point, Line, Plane

  15. Which statement below must be trueabout circle Q? A) The distance from U to W is the same as the distance from R to T. B) The distance from U to W is the same as the distance from Q to J. C) The distance from R to T is half the distance from Q to R. D) The distance from R to T is twice U w the distance from Q to J. Q\ TR Q J Lesson 1-1 Point, Line, Plane

  16. Remember C =πd 2r=d r = 45 in. The radius of a circle is 45 in. Which is a true statement about the circumference (c)? A) c > 6,000 in. and c < 6,500 in. B) c > 250 in. and c < 300 in. C) c > 100 in. and c < 150 in. D) c > 50 in. and c < 100 in. Lesson 1-1 Point, Line, Plane

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