Question

Which of the following must be true? The diagram is not to scale.

A) BC < FH
B) AC = FH
C) AB < BC
D) AC < FH

Answer 1

Answer: Choice D

By the hinge theorem, we know that the opposite side of the given angles will be larger as you increase the angle. Basically think of a door opening. The greater or wide the door is open, the larger the hinge angle leading to a larger distance from door to frame.

We see that angle G = 70 is larger than angle B = 28. So the opposite side HF must be larger than side AC

Note: the hinge theorem only works if we know two pairs of sides are congruent like this