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**intersecting geometric figures in the plane**

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**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

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**How many points of intersection**

can two figures have?

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**In how many points can these two triangles intersect?**

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**In how many points can these two triangles intersect?**

One?

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**In how many points can these two triangles intersect?**

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**In how many points can these two triangles intersect?**

Three?

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**In how many points can these two triangles intersect?**

Four?

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**In how many points can these two triangles intersect?**

Five?

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**In how many points can these two triangles intersect?**

Five?

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**In how many points can these two triangles intersect?**

Six?

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**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

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**Describe the intersection of two geometric figures**

A point An acute angle A segment

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**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

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**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

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

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

Answer: (There is more than one answer!)

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**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?

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One point Two Points Three points Four points

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**Can a triangle and circle intersect in exactly six points?**

Yes!

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**Maximum number of points**

of intersection Two circles? Two triangles? Two pentagons?

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**Maximum number of points**

Two circles? Two triangles? Two pentagons? 2 6 10

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**If a line intersects a triangle in one point, **

what is special about that point?

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**If a line intersects a triangle in one point, **

what is special about that point? The point is a vertex of the triangle.

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**. . . Is there a pattern? Maximum number of points of intersection: 8**

2 triangles 6 2 rectangles 8 2 pentagons 10 . . . 2 hexagons? 2 heptagons?

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2 octagons? 16 points

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THE END By Sandy Christen Oak Ridge Schools

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