Question

Show how it is possible for two triangles to intersect one point, two points, three points, four points, five points, or six points, but not seven points. Show how they can intersect in infinitely many points.

Answer 1

In your question which ask for the how its possible for the two triangles to intersect in one, two, three, four, five, six points but not seven points. Its because the triangles has only 3 sides which means that the intersection that could from in the two is less than 7 or maximum of 6

Answer 2

Answer with explanation:

→There are three sides in a triangle.

So, total number of line segments in two triangles =3 +3=6

→The two line segment can intersect at single point.A transversal can intersect a pair of intersecting lines or non intersecting lines at not more than two points.

So, if you will keep this property in mind, the two lines can intersect at,0, 1 ,2,3,4,5,and 6 points not 7 points.

As there are infinite number of points on the line.So, if one of the sides of two triangles coincide, or two sides coincide, then the intersection of two lines can be infinite number of points.