Question

Order the side lengths , , , , and from least to greatest.

(Note that the figure is not drawn to scale.)

F
G
H
I

Answer 1

Mark the formula/theorem below

• The angle measures bigger means the opposite side of angle is bigger.

Here

• 55<59<63<75

So the order is

• FH<IH<GI<GH<FG

Answer 2

1. FH, 2. GH, 3.IH 4. GI, 5. FG

Explanation:

According to a certain geometric theorem, the smallest angle is always opposite to the smallest side of a triangle. Likewise, the largest angle is always opposite to the largest side. Using this theorem we can properly order the angles and sides.

Additionally, the interior degrees of a triangle will always be 180, and the interior of this quadrilateral is 360 degrees. Using this we can determine the missing angles.

180 - 75 - 55 = 50 (first missing angle)

180 - 59 - 63 = 58 (second missing angle)

The smallest angle would be 50 degrees and the largest 75.

The second smallest is 55 degrees, the third smallest is 58 degrees, the fourth smallest is 59 degrees, and the fifth is 63 degrees.

Now, one thing that seems a bit confusing is the fact that GH is opposite to 2 different angles, so how do we know WHICH angle to use to find its length. From what I understand, we should be able to find the average of the two angles across from this side to see what its place would be in terms of length.

63 + 50 = 56.5

This would make side GH larger than FH but less than HI

This is how I would solve the problem, and I think this is the correct order. Please let me know whether it turns out right.