CK12 - Geometry

Next we havea patternof squaresand triangles.

A. How manytriangleswouldbe in a tenthillustration?

. Thereare squares,with a triangleaboveand beloweachsquare.Thereis also a triangleon each

end of the figure.That makes trianglesin all.

B. One of the figureswouldcontain 34 triangles.How manysquareswouldbe in that figure?

. Take off one trianglefrom eachend. This leaves triangles.Half of these triangles,or trian-

gles,are aboveand trianglesare belowthe squares.This meansthereare squares.

To check:With squares,thereis a triangleaboveand beloweachsquare,making squares.

Add one trianglefor eachend and we have trianglesin all.

C. How can we find the numberof trianglesif we knowthe figurenumber?

Let be the figurenumber. This is also the numberof squares. is the numberof trianglesaboveand

belowthe squares.Add for the triangleson the ends.

If the figurenumberis , then thereare trianglesin all.

Example 3

Now look at a patternof pointsand line segments.

For two points,thereis one line segmentwith thosepointsas endpoints.

For threenoncollinearpoints(pointsthat do not lie on a singleline),thereare threeline segmentswith
thosepointsas endpoints.

A. For four points,no threepointsbeingcollinear, how manyline segmentswith thosepointsas endpoints
are there?