### Video Transcript

In the figure, given that the two
triangles are similar, what is the scale factor that would take you from the larger
triangle to the smaller triangle?

We can recall that the word
“similar” means the same shape but a different size. More specifically, we can say that
corresponding angles are congruent and corresponding sides are in proportion. In order to find the scale factor
that takes us from the large triangle to the small triangle, we need to work out the
proportion of the sides. This ratio or proportion is the
scale factor.

We can start by looking at the base
lengths and using the helpful formula that the scale factor is equal to the new
length over the original length. Then, as the new length in the
smaller triangle is six and the original base length is 12 in the larger triangle,
we have a scale factor of six over 12, which simplifies to one-half. So, each of the lengths in the
smaller triangle will be half of the lengths in the larger triangle.

We can check our answer using the
other pair of given sides. If we take the length of 11 and
multiply it by the scale factor of a half, we would get 11 over two, which
simplifies to five and a half or 5.5. The corresponding length on the
smaller triangle was indeed 5.5. And so, we’ve confirmed our answer
that the scale factor from the larger triangle to the smaller triangle is a
half.

We must always make sure that the
scale factor is a multiplier. So, for example, we could’ve
divided the lengths on the larger triangle by two to get to the smaller
triangle. But our scale factor could not be
“dividing by two.” It would have to be “multiplying by
a half.”