Which statement correctly compares ab and fd?
ab and fd are the same length.
ab is longer than fd.
o
ab is shorter than fd
ab is shorter than or the same length as fd.

AB is longer than FD.

Step-by-step explanation:

This is an SAS triangle problem.

According to the law of cosines,

c^2 = a^2 + b^2 - 2abcosC

In triangle ABC, a = BC, b = AC, and c = AB

In triangle FDE, a = DE, b = FE, and c = FD.

The only difference is that C is 72° in one triangle and 65° in the other.

We know that cos0° = 1 and cos 90° = 0, so cos72° < cos65°.

In triangle ABC, cosC is smaller, so you are subtracting a smaller number from a^2 + b^2.

c^2 is larger, so c is larger.

AB is longer than FD.

That makes sense because, as you widen the angle between your outstretched arms, the distance between your hands increases.