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intersecting geometric figures in the plane

This text explores the intersection points of geometric figures such as triangles, rectangles, pentagons, and circles. It discusses how many points of intersection can occur between two triangles, highlighting the complexity and variability of intersections. The document also poses questions about the nature of intersection points and provides examples to illustrate different scenarios. It emphasizes the maximum possible intersection points and encourages readers to visualize and draw intersections, enhancing their understanding of geometric relationships.

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intersecting geometric figures in the plane

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  1. intersecting geometric figures in the plane

  2. How many points of intersection can two figures have?

  3. In how many points can these two triangles intersect?

  4. In how many points can these two triangles intersect? One?

  5. In how many points can these two triangles intersect? Two?

  6. In how many points can these two triangles intersect? Three?

  7. In how many points can these two triangles intersect? Four?

  8. In how many points can these two triangles intersect? Five?

  9. In how many points can these two triangles intersect? Five?

  10. In how many points can these two triangles intersect? Six?

  11. In how many points can these two triangles intersect? The two triangles can also intersect in a segment

  12. Describe the intersection of two geometric figures A point An acute angle A segment

  13. Here are some for you to try… Look at the two figures. Which could not describe the intersection of these figures? • a line segment • a point • a right angle • a ray

  14. Look at the two figures. Which could not describe the intersection of these figures? Answer: d) a ray a) a line segment c) a right angle b) a point

  15. Draw a rectangle and a triangle intersecting in exactly six points.

  16. Draw a rectangle and a triangle intersecting in exactly six points. Answer: (There is more than one answer!)

  17. Draw a triangle and a circle intersecting in exactly:

  18. One point Two Points Three points Four points

  19. Yes! Can a triangle and circle intersect in exactly six points?

  20. Maximum number of points of intersection Two pentagons? Two triangles? Two circles?

  21. Maximum number of points Two circles? Two triangles? Two pentagons? 2 6 10

  22. If a line intersects a triangle in one point, what is special about that point?

  23. If a line intersects a triangle in one point, what is special about that point? The point is a vertex of the triangle.

  24. Is there a pattern? Maximum number of points of intersection: 2 triangles 2 rectangles 2 pentagons 8 10 6 . . . 2 hexagons? 2 heptagons?

  25. 2 octagons? 16 points

  26. THE END By Sandy Christen Oak Ridge Schools

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