Question

Triangle DEF is similar to triangle ABC. What is the length of segment DE, and what is the length of segment EF? Please explain.

Answer 1

In similar triangles, corresponding sides are proportional. To find the length of segment DE in triangle DEF and the length of segment EF, we can set up a proportion using the corresponding sides of the similar triangles.

Step-by-step explanation:

When two triangles are similar, it means they have the same shape but not necessarily the same size. In similar triangles, corresponding sides are proportional.

Let's say the length of DE in triangle DEF is d and the length of EF is e. If triangle DEF is similar to triangle ABC, then the corresponding sides are proportional. So we have:

DE/AB = EF/BC

Substituting the given values:

d/8 = e/12

Simplifying the equation:

d = (8/12)e

Now we can find the values of d and e by substituting a value for e.