1. intersecting geometric figures in the plane

2. The intersection is the set of points that the figures have in common
Two or more geometric figures intersect if they have one or more points in common
The intersection is the set of points that the figures have in common

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

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

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

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

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

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

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

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

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

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

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

14. 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

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

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

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

18. Draw a triangle and a circle intersecting in exactly:
One point
Two Points
Three points
Four points
Can a triangle and circle intersect in six points?

19. One point
Two Points
Three points
Four points

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

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

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

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

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

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

26. 2 octagons?
16 points

27. THE END
By Sandy Christen
Oak Ridge Schools