Answer:
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.
