Similar Triangles

We built triangles today out of pattern blocks. We looked at how the side lengths scale. The single triangle has a side length of 1, and an area of 1 triangle. We can see that the triangles in the photo have side lengths of 2, 3, and 4, and they have areas of 4 triangles, 9 triangles and 16 triangles.

We made the inference that if we built a triangle that had a side lengths of 5 that it’d take 25 triangle tiles to do it.

We consolidated the idea that if a side lengths scales by the factor k, the area will scale by the factor k squared. We noticed that this connects beautifully to our quadratic patterning that we had been looking at, with a second difference being the same each time, and a graph that is a curve, and the equation would be y=x^2 so there’s an exponent of 2 which indicates that the relationship is quadratic.