intersecting geometric figures in the plane

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Presentation transcript:

intersecting geometric figures in the plane

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

How many points of intersection can two figures have?

In how many points can these two triangles intersect?

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

In how many points can these two triangles intersect?

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

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

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

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

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

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

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

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

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

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

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

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?

One point Two Points Three points Four points

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

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

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

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

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

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

2 octagons? 16 points

THE END By Sandy Christen Oak Ridge Schools