intersecting geometric figures in the plane

How many points of intersectioncan 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?

Two?

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?

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) a line segmentb) a pointc) a right angled) a ray

Look at the two figures. Which could not describe the intersection of these figures?

a) a line segment

Answer: d) a ray

b) a point

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 exactly six points?

Two circles? Two triangles? Two pentagons?

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 vertexof the triangle.

Is there a pattern?Maximum number of points of intersection:

2 triangles

6

2 rectangles

8

2 pentagons

10

. . .2 hexagons? 2 heptagons?

2 octagons?

16 points

By Sandy ChristenOak Ridge Schools