CK12 - Geometry

To solvethis problem,you mustcarefullycountthe trianglesof differentsize. Beginwith the smallesttriangles.
Thereare 16 smalltriangles.

Now countthe trianglesthat are formedby four of the smallertriangles,like the one below.

Thereare a total of seventrianglesof this size,if you rememberto countthe invertedone in the centerof
the diagram.

Next,countthe trianglesthat are formedby nine of the smallertriangles.Thereare threeof thesetriangles.
And finally, thereis one triangleformedby 16 smallertriangles.

Now, add thesenumberstogether.

16 + 7 + 3 + 1 = 27

So, thereare a total of 27 trianglesin the figureshown.

Classificationsby Angles

Earlierin this chapter, you learnedhow to classifyanglesas acute,obtuse,or right.Now that you knowhow
to identifytriangles,we can separatetheminto classificationsas well. One way to classifya triangleis by
the measureof its angles.In any triangle,two of the angleswill alwaysbe acute.This is necessaryto keep
the total sum of the interioranglesat 180º.The third angle,however, can be acute,obtuse,or right.

This is how trianglesare classified.If a trianglehas one right angle,it is calledarighttriangle.