Question

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

A. AB < BC
C. BC < FH
D. AC < FH

Answer 1

I think it would be D) AC<FH

Answer 2

Answer:

D. AC < FH

Step-by-step explanation:

We know that,

Hinge Theorem states that 'if two sides of a triangle are congruent to the two sides of an another triangle and the included angle of the first triangle is larger than the angle of the second triangle, then the third side of the first triangle is greater than the third side of the second triangle'.

Now, according to our figures, we see that,

In ΔABC and ΔHGF, sides AB is congruent to HG and BC is congruent to GF. Also, ∠HGF = 74° and ∠ABC = 31°.

Since, 74 > 31. Therefore, ∠HGF > ∠ABC.

So, according to the 'Hinge Theorem', side FH is greater than AC or AC is less than FH.

Hence, AC < FH.